Capillary condensation - AbsoluteAstronomy.com

Capillary Condensation is the "process by which multilayer adsorption

Adsorption

Adsorption is the adhesion of atoms, ions, biomolecules or molecules of gas, liquid, or dissolved solids to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. It differs from absorption, in which a fluid permeates or is dissolved by a liquid or solid...

from the vapor [phase] into a porous medium

Porous medium

A porous medium is a material containing pores . The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid...

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

Van der Waals force

In physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...

interactions between vapor phase molecules inside the confined space of a capillary. Once condensation has occurred, a meniscus

Meniscus

The meniscus is the curve in the upper surface of a liquid close to the surface of the container or another object, caused by surface tension. It can be either convex or concave. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the material of the...

immediately forms at the liquid-vapor interface which allows for equilibrium

Vapor-liquid equilibrium

Vapor–liquid equilibrium is a condition where a liquid and its vapor are in equilibrium with each other, a condition or state where the rate of evaporation equals the rate of condensation on a molecular level such that there is no net vapor-liquid interconversion...

below the saturation vapor pressure. Meniscus

Meniscus

formation is dependent on the surface tension

Surface tension

Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...

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, the Kelvin equation

Kelvin equation

The Kelvin equation describes the change in vapour pressure due to a curved liquid/vapor interface with radius r . The Kelvin equation is used for determination of pore size distribution of a porous medium using adsorption porosimetry...

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 is an important factor in both naturally occurring and synthetic porous structures. In these structures, scientists use the concept of capillary condensation to determine pore size distribution and surface area

Surface area

Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...

though adsorption isotherms. Synthetic applications such as sintering

Sintering

Sintering is a method used to create objects from powders. It is based on atomic diffusion. Diffusion occurs in any material above absolute zero, but it occurs much faster at higher temperatures. In most sintering processes, the powdered material is held in a mold and then heated to a temperature...

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 and Microelectromechanical Systems

Microelectromechanical systems

Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...

Kelvin equation

The Kelvin equation

Kelvin equation

can be used to describe the phenomenon of capillary condensation due to the presence of a curved meniscus

Meniscus

Where...

= equilibrium vapor pressure

Vapor pressure

Vapor pressure or equilibrium vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system. All liquids have a tendency to evaporate, and some solids can sublimate into a gaseous form...

= saturation vapor pressure

Vapor pressure

= mean curvature

Curvature

In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

of meniscus

Meniscus

= liquid/vapor surface tension

Surface tension

= liquid molar volume

Molar volume

The molar volume, symbol Vm, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density...

= ideal gas constant

= temperature

This equation, shown above, governs all equilibrium systems involving meniscus

Meniscus

and provides mathematical reasoning for the fact that condensation of a given species occurs below the saturation vapor pressure

Vapor pressure

(P_v < P_sat) inside a capillary. At the heart of the Kelvin equation

Kelvin equation

is the pressure difference between the liquid and vapor phases, which comes as a contrast to traditional phase diagrams where phase equilibrium occurs at a single pressure, known as P_sat, for a given temperature. This pressure drop (

) is due solely to the liquid/vapor surface tension

Surface tension

and curvature

Curvature

of the meniscus

Meniscus

, as described in the Young-Laplace equation.

In the Kelvin equation

Kelvin equation

, the saturation vapor pressure

Vapor pressure

, surface tension

Surface tension

, and molar volume

Molar volume

The molar volume, symbol Vm, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density...

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

Kelvin equation

as it is a function of the saturation vapor pressure

Vapor pressure

and vice versa. Therefore, the variables that govern capillary condensation most are the equilibrium vapor pressure

Vapor pressure

and the mean curvature

Curvature

of the meniscus

Meniscus

Dependence of P_v/P_sat

The relation of equilibrium vapor pressure

Vapor pressure

to the saturation vapor pressure can be thought of as a relative humidity

Humidity

Humidity is a term for the amount of water vapor in the air, and can refer to any one of several measurements of humidity. Formally, humid air is not "moist air" but a mixture of water vapor and other constituents of air, and humidity is defined in terms of the water content of this mixture,...

measurement for the atmosphere. As P_v/P_sat increases, vapor will continue to condense inside a given capillary. If P_v/P_sat decreases, liquid will begin to evaporate into the atmosphere as vapor molecules. The figure below demonstrates four different systems in which P_v/P_sat is increasing from left to right.

System A → P_v=0, no vapor is present in the system

System B → P_v=P₁sat, capillary condensation occurs and liquid/vapor equilibrium

Vapor-liquid equilibrium

is reached

System C → P_v=P₂sat, P₁2, as vapor pressure

Vapor pressure

is increased condensation

Condensation

Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....

continues in order to satisfy the Kelvin equation

Kelvin equation

System D → P_v=P_maxsat, vapor pressure

Vapor pressure

is increased to its maximum allowed value and the pore is filled completely

This figure is used to demonstrate the concept that by increasing the vapor pressure

Vapor pressure

in a given system, more condensation will occur. In a porous medium

Porous medium

A porous medium is a material containing pores . The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid...

, capillary condensation will always occur if P_v≠0.

Dependence on curvature

The Kelvin equation

Kelvin equation

indicates that as P_v/P_sat increases inside a capillary, the radius of curvature

Radius of curvature (mathematics)

In geometry, the radius of curvature, R, of a curve at a point is a measure of the radius of the circular arc which best approximates the curve at that point. If this value taken to be positive when the curve turns anticlockwise and negative when the curve turns clockwise...

will also increase, creating a flatter interface. (Note: This is not to say that larger radii of curvature result in more vapor condensation. See the discussion on contact angle below.) Figure 2 above demonstrates this dependence in a simple situation whereby the capillary radius is expanding toward the opening of the capillary and thus vapor condensation occurs smoothly over a range of vapor pressures. In a parallel situation, where the capillary radius is constant throughout its height, vapor condensation would occur much more rapidly, reaching the equilibrium radius of curvature (Kelvin radius) as quickly as possible. This dependence on pore geometry and curvature

Curvature

can result in hysteresis

Hysteresis

Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...

and vastly different liquid/vapor equilibria over very small ranges in pressure.

It is also worthy to mention that different pore geometries result in different types of curvature

Curvature

. In scientific studies of capillary condensation, the hemispherical meniscus

Meniscus

situation (that resulting from a perfectly cylindrical pore) is most often investigated due to its simplicity. Cylindrical menisci are also useful systems because they typically result from scratches, cuts, and slit-type capillaries in surfaces. Many other types of curvature

Curvature

are possible and equations for the curvature

Curvature

of menisci are readily available at numerous sources. Those for the hemispherical and cylindrical menisci are shown below.

General Curvature Equation:

Cylinder:

Hemisphere:

Dependence on contact angle

Contact angle

The contact angle is the angle at which a liquid/vapor interface meets a solid surface. The contact angle is specific for any given system and is determined by the interactions across the three interfaces. Most often the concept is illustrated with a small liquid droplet resting on a flat...

, or wetting angle, is a very important parameter in real systems where perfect wetting

Wetting

Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. The degree of wetting is determined by a force balance between adhesive and cohesive forces.Wetting is important in the bonding or adherence of...

(

= 0^o) is hardly ever achieved. The Young Equation provides reasoning for contact angle

Contact angle

involvement in capillary condensation. The Young Equation explains that the surface tension

Surface tension

between the liquid and vapor phases is scaled to the cosine of the contact angle

Contact angle

. As shown in the figure to the right, the contact angle

Contact angle

between a condensed liquid and the inner wall of a capillary can affect the radius of curvature a great deal. For this reason, contact angle

Contact angle

is coupled inherently to the curvature term of the Kelvin equation

Kelvin equation

. As the contact angle

Contact angle

increases, the radius of curvature

Radius of curvature (mathematics)

will increase as well. This is to say that a system with perfect wetting

Wetting

will exhibit a larger amount of liquid in its pores than a system with non-perfect wetting

Wetting

(

> 0^o). Also, in systems where

= 0^o the radius of curvature is equal to the capillary radius. Due to these complications caused by contact angle

Contact angle

, scientific studies are often designed to assume

= 0^o.

Odd pore geometries

In both naturally occurring and synthetic porous structures, the geometry of pores and capillaries is almost never perfectly cylindrical. Often, porous media contain networks of capillaries, much like a sponge. Since pore geometry affects the shape and curvature of an equilibrium meniscus, the Kelvin equation could be represented differently every time the meniscus changes along a “snake-like” capillary. This makes the analysis via the Kelvin equation complicated very quickly. Adsorption isotherm studies utilizing capillary condensation are still the main method for determining pore size and shape. 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.

Hysteresis

Non-uniform pore geometries often lead to differences in adsorption and desorption pathways within a capillary. This deviation in the two is called a hysteresis and is characteristic of many path dependent processes. For example, if a capillary’s radius increases sharply, then capillary condensation (adsorption) will cease until an equilibrium vapor pressure is reached which satisfies the larger pore radius. However, during evaporation (desorption), liquid will remain filled to the larger pore radius until an equilibrium vapor pressure that satisfies the smaller pore radius is reached. The resulting plot of adsorbed volume versus relative humidity yields a hysteresis “loop.” This loop is seen in all hysteresis governed processes and gives direct meaning the term “path dependent.” 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.

Hysteresis in capillary condensation has been shown to be minimized at higher temperatures.

Accounting for small capillary radii

Capillary condensation in pores with r<10 nm is often difficult to describe using the Kelvin equation. This is because the Kelvin equation underestimates the size of the pore radius when working on the nanometer scale. To account for this underestimation, the idea of a statistical film thickness, t, has often been invoked. 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. The figure to the left gives an explanation of the statistical film thickness in relation to the radius of curvature for the meniscus. 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. At very small pore radii though, the film thickness becomes an important factor in accurately determining the pore radius.

Bridging effects

Starting from the assumption that two wetted surfaces will stick together, e.g. the bottom of a glass cup on a wet counter top, will help to explain the idea of how capillary condensation causes two surfaces to bridge together. When looking at the Kelvin equation, where relative humidity comes into play, condensation that occurs below P_sat will cause adhesion. However it is most often ignored that the adhesive force is dependent only on the particle radius (for wettable, spherical particles, at least) and therefore independent of the relative vapor pressure or humidity, within very wide limits. 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. Experimentally, however it is seen that capillary condensation plays a large role in bridging or adhering multiple surfaces or particles together. This can be important in the adhesion of dust and powders. It is important to note the difference between bridging and adhesion. 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

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.

Atomic force microscopy

Capillary condensation bridges two surfaces together, with the formation of a meniscus

Meniscus

, as is stated above. While this is sometimes a desirable effect, in the case of Atomic Force Microscopy (AFM) this is an exceedingly undesirable consequence. AFM is generally operated in one of two main modes, contact mode and non-contact mode. While studies have been done on the formation of the meniscus

Meniscus

between the tip and the sample, no concrete conclusion can be drawn as to the optimum height away from the sample the tip can be without this side effect occurring. Scientific studies have been done on the relation between relative humidity and the height of the meniscus

Meniscus

created by capillary condensation. One particular study, done by Weeks, illustrated that with the increase in relative humidity, there is a large increase in the size of the meniscus

Meniscus

. This study also states that no meniscus

Meniscus

formation is observed when the relative humidity is less than 70%, although there is uncertainty in this conclusion due to limits of resolution. The meniscus

Meniscus

effect with AFM is rather detrimental because of the hard time that AFM already has with accurate information in the x and y planes of the sample. Meniscus

Meniscus

formation causes the tip to have an elongated geometry which in turn distorts the already semi-inaccurate information gathered from the x and y directions.

Although undesirable for imaging purposes, the formation of the meniscus is the basis of the Dip-Pen Nanolithography technique.

Sintering

is a common practice used widely with both metals and ceramic

Ceramic

A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...

materials. Sintering

Sintering

is a direct application of capillary condensation, because of the adhesion effects of dust and powders. This application can be seen directly in sol-gel thin film synthesis. The sol-gel is a colloid

Colloid

A colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...

solution which is placed on a substrate, usually through a dip-coating method. After being placed onto the substrate, a source of heat is applied to evaporate all undesired liquid. While the liquid is evaporating, the particles that were once in solution adhere to each other, thus forming a thin film.

MEMS

Microelectromechanical systems

Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...

(MEMS) are used in a number of different applications and have become increasingly more prevalent in nanoscale applications. However, due to their small size they run into problems with stiction

Stiction

Stiction is the static friction that needs to be overcome to enable relative motion of stationary objects in contact. The term is a portmanteau of the term "static friction", perhaps also influenced by the verb "stick"....

, caused by capillary condensation among other forces. Intense research in the area of Microelectromechanical systems

Microelectromechanical systems

Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...

has been focused on finding ways to reduce stiction

Stiction

in the fabrication of Microelectromechanical systems

Microelectromechanical systems

Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...

and when they are being used. Srinivasan et al. did a study in 1998 looking at applying different types of Self-assembled monolayers (SAMs) to the surfaces of Microelectromechanical systems

Microelectromechanical systems

Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...

in hopes of reducing stiction

Stiction

or getting rid of it altogether. They found that using OTS (octadecyltrichlorosilane) coatings reduced both types of stiction

Stiction

Pore size distribution

Pores that are not of the same size will fill at different values of pressure, with the smaller ones filling first. This difference in filling rate can be a beneficial application of capillary condensation. Many materials have different pore sizes with ceramics being one of the most commonly encountered. In materials with different pore sizes, curves can be constructed similar to Figure 7. A detailed analysis of the shape of these isotherms is done using the Kelvin equation

Kelvin equation

. This enables the pore size distribution to be determined. While this is a relatively simple method of analyzing the isotherms, a more in depth analysis of the isotherms is done using the BET

BET theory

BET theory aims to explain the physical adsorption of gas molecules on a solid surface and serves as the basis for an important analysis technique for the measurement of the specific surface area of a material...

method. Another method of determining the pore size distribution is by using a procedure known as Mercury Injection Porosimetry. This uses the volume of mercury taken up by the solid as the pressure increases to create the same isotherms mentioned above. An application where pore size is beneficial is in regards to oil recovery. When recovering oil from tiny pores, it is useful to inject gas and water 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 it to leave the pore.

External links

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Kelvin equation

Dependence of Pv/Psat

Dependence on curvature

Dependence on contact angle

Odd pore geometries

Hysteresis

Accounting for small capillary radii

Bridging effects

Atomic force microscopy

Sintering

MEMS

Pore size distribution

See also

External links

Dependence of P_v/P_sat