In
materials science
Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries.
The intellectual origins of materials sci ...
and
biology
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
, capillary condensation is the "process by which multilayer
adsorption
Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a ...
from the
vapor
In physics, a vapor (American English) or vapour (Commonwealth English; American and British English spelling differences#-our, -or, see spelling differences) is a substance in the gas phase at a temperature lower than its critical temperature,R ...
haseinto a
porous medium
In materials science, a porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The sk ...
proceeds to the point at which pore spaces become filled with condensed
liquid
Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...
from the vapor
hase"
[Schramm, L.L ''The Language of Colloid & Interface Science'' 1993, ACS Professional Reference Book, ACS: Washington, D.C.] The unique aspect of capillary
condensation
Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...
is that vapor condensation occurs below the
saturation vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
, , of the pure liquid.
[Hunter, R.J. ''Foundations of Colloid Science'' 2nd Edition, Oxford University Press, 2001.] 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
Equilibrium may refer to:
Film and television
* ''Equilibrium'' (film), a 2002 science fiction film
* '' The Story of Three Loves'', also known as ''Equilibrium'', a 1953 romantic anthology film
* "Equilibrium" (''seaQuest 2032'')
* ''Equilibr ...
below the saturation vapor pressure. Meniscus formation is dependent on the
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
of the liquid and the shape of the capillary, as shown by the
Young-Laplace equation. As with any liquid-vapor interface involving a meniscus, the
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
provides a relation for the difference between the equilibrium vapor pressure and the saturation vapor pressure.
[Casanova, F. ''et al.'' ''Nanotechnology'' 2008, Vol. 19, 315709.][Kruk, M. ''et al.'' ''Langmuir'' 1997, 13, 6267-6273.][Miyahara, M. ''et al.'' ''Langmuir'' 2000, 16, 4293-4299.][Morishige, K. ''et al.'' ''Langmuir'' 2006, 22, 4165-4169.] 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
The surface area (symbol ''A'') of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the d ...
through adsorption isotherms.
Synthetic applications such as
sintering
Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing process used with metals, ceramics, plas ...
[Kumagai, M; Messing, G. L. ''J. Am. Ceramic Soc.'' 1985, 68, 500-505.] 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
Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the opti ...
[Weeks, B. L.; Vaughn, M. W.; DeYoreo, J. J. ''Langmuir'', 2005, 21, 8096-8098.] and
microelectromechanical systems
MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
.
[Srinivasan, U.; Houston, M. R.; Howe, R. T.; Maboudian, R. ''Journal of Microelectromechanical Systems'', 1998, 7, 252-260.]
Kelvin equation
The
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
can be used to describe the phenomenon of capillary condensation due to the presence of a curved
meniscus.
::
Where...
:
= equilibrium
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
:
= saturation
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
:
= mean
curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
of
meniscus
:
= liquid/vapor
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
:
= liquid
molar volume
In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume (''V'') occupied by a substance to the amount of substance (''n''), usually at a given temperature and pressure. It is also eq ...
:
=
ideal gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment pe ...
:
= temperature
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
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
(P
v < P
sat) inside a capillary. At the heart of the
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
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 is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
and
curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
of the
meniscus, as described in the
Young-Laplace equation.
::
In the
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
, the saturation
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
,
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
, and
molar volume
In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume (''V'') occupied by a substance to the amount of substance (''n''), usually at a given temperature and pressure. It is also eq ...
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
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
as it is a function of the saturation
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
and
vice versa. Therefore, the variables that govern capillary condensation most are the equilibrium
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
and the mean
curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
of the
meniscus.
Dependence of Pv/Psat
The relation of equilibrium
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
to the
saturation vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
can be thought of as a relative
humidity
Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation (meteorology), precipitation, dew, or fog t ...
measurement for the atmosphere. As P
v/P
sat increases, vapor will continue to
condense
Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...
inside a given capillary. If P
v/P
sat decreases, liquid will begin to
evaporate
Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. A high concentration of the evaporating substance in the surrounding gas significantly slows down evaporation, such as when hum ...
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=P
1sat, capillary condensation occurs and liquid/vapor
equilibrium
Equilibrium may refer to:
Film and television
* ''Equilibrium'' (film), a 2002 science fiction film
* '' The Story of Three Loves'', also known as ''Equilibrium'', a 1953 romantic anthology film
* "Equilibrium" (''seaQuest 2032'')
* ''Equilibr ...
is reached
System C → P
v=P
2sat, P1
2, as
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
is increased
condensation
Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...
continues in order to satisfy the
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
System D → P
v=P
maxsat,
vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
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 or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indicat ...
in a given system, more condensation will occur. In a
porous medium
In materials science, a porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The sk ...
, capillary condensation will always occur if P
v≠0.
Dependence on curvature
The
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
indicates that as P
v/P
sat increases inside a capillary, the
radius of curvature
In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius ...
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
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
can result in
hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
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
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
. 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.
Cylindrical
menisci are also useful systems because they typically result from scratches, cuts, and slit-type capillaries in surfaces. Many other types of
curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
are possible and equations for the
curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
of
menisci are readily available at numerous sources.
[A Practical Guide to Isotherms of Adsorption on Heterogeneous Surfaces](_blank)
Marczewski, A. M., 2002. Those for the hemispherical and cylindrical
menisci are shown below.
General Curvature Equation:
::
Cylinder:
::
Hemisphere:
::
Dependence on contact angle
Contact angle
The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
, or
wetting angle, is a very important parameter in real systems where perfect
wetting
Wetting is the ability of a liquid to displace gas to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. These interactions occur in the presence of either a gaseous phase or ...
(
= 0
o) is hardly ever achieved. The
Young equation provides reasoning for
contact angle
The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
involvement in capillary condensation. The Young Equation explains that the
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
between the liquid and vapor phases is scaled to the cosine of the
contact angle
The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
. As shown in the figure to the right, the
contact angle
The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
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
The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
is coupled inherently to the curvature term of the
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
. As the
contact angle
The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
increases, the
radius of curvature
In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius ...
will increase as well. This is to say that a system with perfect
wetting
Wetting is the ability of a liquid to displace gas to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. These interactions occur in the presence of either a gaseous phase or ...
will exhibit a larger amount of liquid in its pores than a system with non-perfect
wetting
Wetting is the ability of a liquid to displace gas to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. These interactions occur in the presence of either a gaseous phase or ...
(
> 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
The contact angle (symbol ) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interfac ...
, scientific studies are often designed to assume
= 0
o.
Non-uniform pore effects
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.
[Vidales, A.M.; Faccio, R.J.; Zgrablich, G.J. ''J. Phys. Condens. Matter'' 1995, 7, 3835-3843.] 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.
[Burgess, C. G. V. ''et al.'' ''Pure Appl. Chem.'' 1989, 61, 1845-1852.]
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.
Capillary adhesion
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
A bridge is a structure built to Span (engineering), span a physical obstacle (such as a body of water, valley, road, or railway) without blocking the path underneath. It is constructed for the purpose of providing passage over the obstacle, whi ...
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 or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing process used with metals, ceramics, plas ...
; 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.
Real-world applications and problems
Atomic-force microscopy
Capillary condensation
bridges
A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or railway) without blocking the path underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually somet ...
two surfaces together, with the formation of a
meniscus, as is stated above. In the case of
atomic-force microscopy
Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the opti ...
(AFM) a capillary bridge of water can form between the tip and the surface, especially in cases of a hydrophilic surface in a humid environment when the AFM is operated in
contact mode. While studies have been done on the formation of the
meniscus between the tip and the sample, no specific conclusion can be drawn as to the optimum height away from the sample the tip can be without
meniscus formation. Scientific studies have been done on the relationship between relative humidity and the geometry of the
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. 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.
The formation of the meniscus is the basis of the
Dip-Pen Nanolithography technique.
Sintering
Sintering
Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing process used with metals, ceramics, plas ...
is a common practice used widely with both metals and
ceramic
A ceramic is any of the various hard, brittle, heat-resistant, and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcela ...
materials.
Sintering
Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing process used with metals, ceramics, plas ...
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
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others exte ...
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
MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
(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 (a portmanteau of the words '' static'' and ''friction'') is the force that needs to be overcome to enable relative motion of stationary objects in contact.
Any solid objects pressing against each other (but not sliding) will require some ...
, caused by capillary condensation among other forces. Intense research in the area of
Microelectromechanical systems
MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
has been focused on finding ways to reduce
stiction
Stiction (a portmanteau of the words '' static'' and ''friction'') is the force that needs to be overcome to enable relative motion of stationary objects in contact.
Any solid objects pressing against each other (but not sliding) will require some ...
in the fabrication of
Microelectromechanical systems
MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
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
MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
in hopes of reducing
stiction
Stiction (a portmanteau of the words '' static'' and ''friction'') is the force that needs to be overcome to enable relative motion of stationary objects in contact.
Any solid objects pressing against each other (but not sliding) will require some ...
or getting rid of it altogether.
They found that using OTS (octadecyltrichlorosilane) coatings reduced both types of
stiction
Stiction (a portmanteau of the words '' static'' and ''friction'') is the force that needs to be overcome to enable relative motion of stationary objects in contact.
Any solid objects pressing against each other (but not sliding) will require some ...
.
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
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
. 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 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.
[Tehrani, D. H.; Danesh, A.; Sohrabi, M.; Henderson, G. ''Enhanced Oil Recovery by Water Alternating Gas (WAG) Injection'' SPE, 2001.] 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.
See also
*
Adsorption
Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a ...
*
Atomic-force microscopy
Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the opti ...
*
BET theory
Brunauer–Emmett–Teller (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 materials. The obs ...
*
Capillarity
Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space without the assistance of external forces like Gravitation, gravity.
The effe ...
*
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
*
Capillary bridges
*
Disjoining pressure
In surface chemistry, disjoining pressure (symbol ) according to an IUPAC definition arises from an attractive interaction between two surfaces. For two flat and parallel surfaces, the value of the disjoining pressure (i.e., the force per unit are ...
*
Kelvin equation
The kelvin (symbol: K) is the SI base unit, base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute scale, absolute temperature scale that starts at the lowest possible temperature (absolute zero), ...
*
Self-assembled monolayers
*
Sintering
Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing process used with metals, ceramics, plas ...
*
Microelectromechanical systems
MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
*
Meniscus (liquid)
In physics (particularly liquid statics), the meniscus (: menisci, ) is the curve in the upper surface of a liquid close to the surface of the container or another object, produced by surface tension.
A concave meniscus occurs when the attract ...
*
Sol-gel
*
Colloid
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others exte ...
*
Ceramic
A ceramic is any of the various hard, brittle, heat-resistant, and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcela ...
External links
A Practical Guide to Isotherms of Adsorption on Heterogeneous Surfaces
References
{{DEFAULTSORT:Capillary Condensation
Fluid dynamics