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| [[Image:porous medium.png|thumb|right|400px|'''Figure 1''': An example of a porous structure exhibiting capillary condensation.]]
| | CMS provides the best platform to create websites that fulfill all the specifications of SEO. The next step is to visit your Word - Press blog dashboard. These templates are professionally designed and are also Adsense ready. Word - Press also provides protection against spamming, as security is a measure issue. It's as simple as hiring a Wordpress plugin developer or learning how to create what is needed. <br><br>Right starting from social media support to search engine optimization, such plugins are easily available within the Word - Press open source platform. The higher your blog ranks on search engines, the more likely people will find your online marketing site. There are number of web services that offer Word press development across the world. Furthermore, with the launch of Windows 7 Phone is the smart phone market nascent App. If you want to find more info regarding [http://scridle.nl/wordpress_backup_plugin_639936 wordpress backup plugin] visit our web site. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself. <br><br>The least difficult and very best way to do this is by acquiring a Word - Press site. s cutthroat competition prevailing in the online space won. all the necessary planning and steps of conversion is carried out in this phase, such as splitting, slicing, CSS code, adding images, header footer etc. The animation can be quite subtle these as snow falling gently or some twinkling start in the track record which are essentially not distracting but as an alternative gives some viewing enjoyment for the visitor of the internet site. Converting HTML to Word - Press theme for your website can allow you to enjoy the varied Word - Press features that aid in consistent growth your online business. <br><br>The primary differences are in the plugins that I install, as all sites don't need all the normal plugins. Russell HR Consulting provides expert knowledge in the practical application of employment law as well as providing employment law training and HR support services. One of the great features of Wordpress is its ability to integrate SEO into your site. It supports backup scheduling and allows you to either download the backup file or email it to you. OSDI, a Wordpress Development Company based on ahmedabad, India. <br><br>Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. with posts or testimonials updated as they are uploaded to a particular section of the website. Press CTRL and the numbers one to six to choose your option. |
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| '''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]."<ref name="schramm">Schramm, L.L ''The Language of Colloid & Interface Science'' '''1993''', ACS Professional Reference Book, ACS: Washington, DC.</ref> The unique aspect of capillary condensation is that vapor condensation occurs below the [[saturation vapor pressure]], P<sub>sat</sub>, of the pure liquid.<ref name="hunter">Hunter, R.J. ''Foundations of Colloid Science'' 2nd Edition, Oxford University Press, '''2001'''.</ref> This result is due to an increased number of [[Van der Waals force|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 [[Vapor-liquid equilibrium|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, the [[Kelvin equation]] provides a relation for the difference between the equilibrium vapor pressure and the saturation vapor pressure.<ref name="casanova">Casanova, F. ''et al.'' ''Nanotechnology'' '''2008''', Vol. 19, 315709.</ref><ref name="kruk">Kruk, M. ''et al.'' ''Langmuir'' '''1997''', 13, 6267-6273.</ref><ref name="miyahara">Miyahara, M. ''et al.'' ''Langmuir'' '''2000''', 16, 4293-4299.</ref><ref name="morishige">Morishige, K. ''et al.'' ''Langmuir'' '''2006''', 22, 4165-4169.</ref> A capillary does not necessarily have to be a tubular, closed shape, but can be any confined space with respect to its surroundings.
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| 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]] though adsorption isotherms.<ref name="casanova"/><ref name="kruk"/><ref name="miyahara"/><ref name="morishige"/> Synthetic applications such as [[sintering]]<ref name="kumagai">Kumagai, M; Messing, G. L. ''J. Am. Ceramic Soc.'' '''1985''', 68, 500-505.</ref> 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]]<ref name="AFM">Weeks, B. L.; Vaughn, M. W.; DeYoreo, J. J. ''Langmuir'', '''2005''', 21, 8096-8098.</ref> and [[Microelectromechanical Systems]].<ref name="MEMS">Srinivasan, U.; Houston, M. R.; Howe, R. T.; Maboudian, R. ''Journal of Microelectromechanical Systems'', '''1998''', 7, 252-260.</ref>
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| ==Kelvin equation==
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| The [[Kelvin equation]] can be used to describe the phenomenon of capillary condensation due to the presence of a curved [[meniscus]].<ref name="hunter"/>
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| ::<math>\ln\frac{P_v}{P_{sat}}=-\frac{2H\gamma V_l}{RT}\ </math>
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| Where...
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| :<math>\ P_v</math> = equilibrium [[vapor pressure]]
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| :<math>\ P_{sat}</math> = saturation [[vapor pressure]]
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| :<math>\ H</math> = mean [[curvature]] of [[meniscus]]
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| :<math>\ \gamma</math> = liquid/vapor [[surface tension]]
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| :<math>\ V_l</math> = liquid [[molar volume]]
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| :<math>\ R</math> = [[ideal gas constant]]
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| :<math>\ T</math> = temperature
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| 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]] (P<sub>v</sub> < P<sub>sat</sub>) inside a capillary. At the heart of the [[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<sub>sat</sub>, for a given temperature. This pressure drop (<math>\scriptstyle \Delta P</math>) is due solely to the liquid/vapor [[surface tension]] and [[curvature]] of the [[meniscus]], as described in the [[Young-Laplace equation]].<ref name="hunter"/>
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| ::<math>\ \Delta P = 2H\gamma</math>
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| 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 [[List of Latin phrases: V#vice versa|vice versa]]. Therefore, the variables that govern capillary condensation most are the equilibrium [[vapor pressure]] and the mean [[curvature]] of the [[meniscus]].
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| ===Dependence of P<sub>v</sub>/P<sub>sat</sub>===
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| The relation of equilibrium [[vapor pressure]] to the [[saturation vapor pressure]] can be thought of as a relative [[humidity]] measurement for the atmosphere. As P<sub>v</sub>/P<sub>sat</sub> increases, vapor will continue to [[condense]] inside a given capillary. If P<sub>v</sub>/P<sub>sat</sub> decreases, liquid will begin to [[evaporate]] into the atmosphere as vapor molecules.<ref name="hunter"/> The figure below demonstrates four different systems in which P<sub>v</sub>/P<sub>sat</sub> is increasing from left to right. | |
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| [[Image:capillary condensation.jpg|thumb|left|500px|'''Figure 2''': Four different capillary systems with increasing P<sub>v</sub> from A to D.]]
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| '''System A''' → P<sub>v</sub>=0, no vapor is present in the system
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| '''System B''' → P<sub>v</sub>=P<sub>1</sub><P<sub>sat</sub>, capillary condensation occurs and liquid/vapor [[Vapor-liquid equilibrium|equilibrium]] is reached
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| '''System C''' → P<sub>v</sub>=P<sub>2</sub><P<sub>sat</sub>, P<sub>1</sub><P<sub>2</sub>, as [[vapor pressure]] is increased [[condensation]] continues in order to satisfy the [[Kelvin equation]]
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| '''System D''' → P<sub>v</sub>=P<sub>max</sub><P<sub>sat</sub>, [[vapor pressure]] is increased to its maximum allowed value and the pore is filled completely
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| This figure is used to demonstrate the concept that by increasing the [[vapor pressure]] in a given system, more condensation will occur. In a [[porous medium]], capillary condensation will always occur if P<sub>v</sub>≠0.
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| ===Dependence on curvature===
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| The [[Kelvin equation]] indicates that as P<sub>v</sub>/P<sub>sat</sub> increases inside a capillary, the [[Radius of curvature (mathematics)|radius of curvature]] 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.<ref name="hunter"/> This dependence on pore geometry and [[curvature]] can result in [[hysteresis]] and vastly different liquid/vapor equilibria over very small ranges in pressure.
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| It is also worthy to mention that different pore geometries result in different types of [[curvature]]. 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.<ref name="miyahara"/> Cylindrical [[menisci]] are also useful systems because they typically result from scratches, cuts, and slit-type capillaries in surfaces. Many other types of [[curvature]] are possible and equations for the [[curvature]] of [[menisci]] are readily available at numerous sources.<ref name="miyahara"/><ref name="adsorption">[http://adsorption.org/awm/ads/Ads-prev.htm A Practical Guide to Isotherms of Adsorption on Heterogeneous Surfaces] Marczewski, A. M., '''2002'''.</ref> Those for the hemispherical and cylindrical [[menisci]] are shown below.
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| '''General Curvature Equation:'''
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| ::<math>\ H = \frac{1}{2}(\frac{1}{R_1}+\frac{1}{R_2})</math>
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| '''Cylinder:''' <math>\ R_1 = r</math> <math>\ R_2 = \infty</math>
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| ::<math>\ H = \frac{1}{2r}</math>
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| '''Hemisphere:''' <math>\ R_1 = r</math> <math>\ R_2 = r</math>
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| ::<math>\ H = \frac{1}{r}</math>
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| ===Dependence on contact angle===
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| [[Image:curvature and contact angle.png|thumb|right|150px|'''Figure 3''': Figure demonstrating the meaning of contact angle inside a capillary as well as the radius of curvature for a meniscus.]]
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| [[Contact angle]], or [[wetting angle]], is a very important parameter in real systems where perfect [[wetting]] (<math>\ \theta</math> = 0<sup>o</sup>) is hardly ever achieved. The [[Wetting#Simplification_to_planar_geometry.2C_Young.27s_relation|Young Equation]] provides reasoning for [[contact angle]] involvement in capillary condensation. 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. For this reason, [[contact angle]] is coupled inherently to the curvature term of the [[Kelvin equation]]. As the [[contact angle]] increases, the [[Radius of curvature (mathematics)|radius of curvature]] will increase as well. This is to say that a system with perfect [[wetting]] will exhibit a larger amount of liquid in its pores than a system with non-perfect [[wetting]] (<math>\ \theta</math> > 0<sup>o</sup>). Also, in systems where <math>\ \theta</math> = 0<sup>o</sup> the radius of curvature is equal to the capillary radius.<ref name="hunter"/> Due to these complications caused by [[contact angle]], scientific studies are often designed to assume <math>\ \theta</math> = 0<sup>o</sup>.<ref name="casanova"/><ref name="kruk"/><ref name="miyahara"/><ref name="morishige"/>
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| ==Non-uniform pore effects==
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| ===Odd pore geometries===
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| 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.<ref name="vidalest">Vidalest, A.M.; Faccio, R.J.; Zgrablich, G.J. ''J. Phys. Condens. Matter'' '''1995''', 7, 3835-3843.</ref> 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.<ref name="vidalest"/> 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.<ref name="casanova"/>
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| ===Hysteresis===
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| 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.”<ref name="hunter"/> 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.
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| Hysteresis in capillary condensation has been shown to be minimized at higher temperatures.<ref name="burgess">Burgess, C. G. V. ''et al.'' ''Pure & Appl. Chem.'' '''1989''', 61, 1845-1852.</ref>
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| ===Accounting for small capillary radii===
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| [[Image:statistical film thickness.png|thumb|left|150px|'''Figure 4''': Figure explaining the term "statistical film thickness" in the context of very small capillary radii.]]
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| 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.<ref name="casanova"/><ref name="kruk"/><ref name="miyahara"/><ref name="morishige"/> 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.
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| ==Capillary adhesion==
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| ===Bridging effects===
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| [[Image:two circles 2.png|thumb|right|150px|'''Figure 5''': Figure demonstrating the bridging between two spheres due to capillary condensation.]]
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| 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<sub>sat</sub> will cause adhesion.<ref name="hunter"/> 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.<ref name="hunter"/> 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.<ref name="hunter"/> 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]]; 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.
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| ==Real-world applications and problems==
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| ===Atomic force microscopy===
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| {{main|Atomic Force Microscopy}}
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| [[Image:meniscus afm picture 2.png|thumb|right|250px|'''Figure 6''': [[Meniscus]] formation between an [[Atomic force microscopy|AFM]] tip and a substrate.]]
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| Capillary condensation bridges two surfaces together, with the formation of a [[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. [[Atomic force microscopy|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]] 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]] created by capillary condensation. One particular study, done by Weeks,<ref name="AFM"/> 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 [[meniscus]] effect with [[Atomic force microscopy|AFM]] is rather detrimental because of the hard time that [[Atomic force microscopy|AFM]] already has with accurate information in the x and y planes of the sample. [[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.
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| Although undesirable for imaging purposes, the formation of the meniscus is the basis of the [[Dip-Pen Nanolithography]] technique.
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| ===Sintering===
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| {{main|Sintering}}
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| [[Image:capillary adsorption profile.png|thumb|right|325px|'''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)]]
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| [[Sintering]] is a common practice used widely with both metals and [[ceramic]] materials. [[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.<ref name="kumagai"/> The [[sol-gel]] is a [[colloid]] 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.
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| ===MEMS===
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| {{main|Microelectromechanical Systems}}
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| [[Microelectromechanical systems]] (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]], caused by capillary condensation among other forces. Intense research in the area of [[Microelectromechanical systems]] has been focused on finding ways to reduce [[stiction]] in the fabrication of [[Microelectromechanical systems]] 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]] in hopes of reducing [[stiction]] or getting rid of it altogether.<ref name="MEMS"/> They found that using OTS (octadecyltrichlorosilane) coatings reduced both types of [[stiction]].
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| ===Pore size distribution===
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| Pores that are not of the same size will fill at different values of pressure, with the smaller ones filling first.<ref name="hunter"/> 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]]. This enables the pore size distribution to be determined.<ref name="hunter"/> While this is a relatively simple method of analyzing the isotherms, a more in depth analysis of the isotherms is done using the [[BET theory|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.<ref name="tehrani">Tehrani, D. H.; Danesh, A.; Sohrabi, M.; Henderson, G. ''Enhanced Oil Recovery by Water Alternating Gas (WAG) Injection'' SPE, '''2001'''.</ref> 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.<ref name="tehrani"/>
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| ==See also==
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| *[[Adsorption]]
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| *[[Atomic Force Microscopy]]
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| *[[BET theory]]
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| *[[Capillarity]]
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| *[[Curvature]]
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| *[[Disjoining pressure]]
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| *[[Kelvin equation]]
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| *[[Self-assembled monolayers]]
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| *[[Sintering]]
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| *[[Microelectromechanical systems]]
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| *[[Meniscus]]
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| *[[Sol-gel]]
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| *[[Colloid]]
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| *[[Ceramic]]
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| ==External links==
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| *[http://adsorption.org/awm/ads/Ads-prev.htm A Practical Guide to Isotherms of Adsorption on Heterogeneous Surfaces]
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| *[http://www.jhu.edu/~chem/fairbr/teach/BET/derive.html Langmuir/BET Derivation]
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| ==References==
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| {{reflist|30em}}
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| {{DEFAULTSORT:Capillary Condensation}}
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| [[Category:Fluid dynamics]]
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CMS provides the best platform to create websites that fulfill all the specifications of SEO. The next step is to visit your Word - Press blog dashboard. These templates are professionally designed and are also Adsense ready. Word - Press also provides protection against spamming, as security is a measure issue. It's as simple as hiring a Wordpress plugin developer or learning how to create what is needed.
Right starting from social media support to search engine optimization, such plugins are easily available within the Word - Press open source platform. The higher your blog ranks on search engines, the more likely people will find your online marketing site. There are number of web services that offer Word press development across the world. Furthermore, with the launch of Windows 7 Phone is the smart phone market nascent App. If you want to find more info regarding wordpress backup plugin visit our web site. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself.
The least difficult and very best way to do this is by acquiring a Word - Press site. s cutthroat competition prevailing in the online space won. all the necessary planning and steps of conversion is carried out in this phase, such as splitting, slicing, CSS code, adding images, header footer etc. The animation can be quite subtle these as snow falling gently or some twinkling start in the track record which are essentially not distracting but as an alternative gives some viewing enjoyment for the visitor of the internet site. Converting HTML to Word - Press theme for your website can allow you to enjoy the varied Word - Press features that aid in consistent growth your online business.
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Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. with posts or testimonials updated as they are uploaded to a particular section of the website. Press CTRL and the numbers one to six to choose your option.