Gauss–Markov process: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Yobot
m WP:CHECKWIKI error fixes - Replaced special characters in sortkey using AWB (9095)
en>Mark viking
top: Added another general ref
Line 1: Line 1:
A '''monolayer''' is a single, closely packed layer of atoms, molecules,<ref>{{cite journal |last1=Ter Minassian-Saraga |first1=L. |year=1994 |title=Thin films including layers: terminology in relation to their preparation and characterization (IUPAC Recommendations 1994) |journal=[[Pure and Applied Chemistry]] |volume=66 |issue=8 |pages=1667–1738 |publisher=[[IUPAC]] |doi=10.1351/pac199466081667 |url=http://pac.iupac.org/publications/pac/pdf/1994/pdf/6608x1667.pdf |accessdate=November 5, 2012}} On page 1672.</ref> or cells. In some cases it is referred to as a [[Self-assembled monolayer]].
I'm a 30 years old and working at the university (Neuroscience).<br>In my spare time I'm trying to teach myself Swedish. I've been  there and look forward to go there sometime near future. I like to read, preferably on my kindle. I really love to watch The Vampire Diaries and Game of Thrones as well as docus about anything astronomical. [http://www.Adobe.com/cfusion/search/index.cfm?term=&I+enjoy&loc=en_us&siteSection=home I enjoy] Art collecting.<br><br>


== Chemistry ==
Feel free to surf to my website; Fifa 15 Coin Generator; [http://Www.Gesinvalles.es/userinfo.php?uid=299374 Gesinvalles.Es],
A '''Langmuir monolayer''' or insoluble monolayer is a one-molecule thick layer of an insoluble organic material spread onto an [[aqueous]] sub[[phase (matter)|phase]]. Traditional compounds used to prepare [[Langmuir (unit)|Langmuir]] monolayers are [[amphiphilic]] materials that possess a [[hydrophilic]] headgroup and a [[hydrophobic]] tail. Since the 1980s a large number of other materials have been employed to produce Langmuir monolayers, some of which are semi-amphiphilic, including [[macromolecule]]s such as [[polymer]]s. Langmuir monolayers are extensively studied for the fabrication of [[Langmuir-Blodgett film]] (LB films), which are formed by transferred monolayers on a solid substrate. A [[Josiah Willard Gibbs|Gibbs]] monolayer or soluble monolayer is a monolayer formed by a compound that is soluble in one of the phases separated by the [[interface (chemistry)|interface]] on which the monolayer is formed.
 
=== Formation time ===
The '''monolayer formation time''' or '''monolayer time''' is the length of time required, on average, for a surface to be covered by an adsorbate, such as oxygen sticking to fresh aluminum. If the adsorbate has a unity [[sticking coefficient]], so that every molecule which reaches the surface sticks to it without re-evaporating, then the monolayer time is very roughly:
:<math>t = \frac{3 \times 10^{-4} \, \mathrm{Pa} \times \mathrm{s}}{P}</math>
where ''t'' is the time and ''P'' is the pressure. It takes about 1 second for a surface to be covered at a pressure of 300&nbsp;µPa (2×10<sup>-6</sup>&nbsp;Torr).
 
=== Monolayer phases and equations of state ===
 
A Langmuir monolayer can be compressed or expanded by modifying its area with a moving barrier in a Langmuir film balance. If the surface tension of the interface is measured during the compression, a ''compression isotherm'' is obtained. This isotherm shows the variation of surface pressure (<math>\Pi = \gamma^o - \gamma </math>, where <math>\gamma^o</math> is the surface tension of the interface before the monolayer is formed) with the area (the inverse of surface concentration <math>\Gamma^{-1}</math>). It is analogous with a 3D process in which [[pressure]] varies with [[volume]].
 
A variety of bidimensional [[phase (matter)|phases]] can be detected, each separated by a [[phase transition]]. During the phase transition, the surface pressure doesn't change, but the area does, just like during normal phase transitions volume changes but pressure doesn't.
The 2D phases, in increasing pressure order:
* Bidimensional gas: there are few molecules per area unit, and they have few interactions, therefore, analogous of the [[equation of state|equations of state]] for 3D gases can be used: ideal gas law <math>\Pi A = RT</math>, where <math>A</math> is the area per mole. As the surface pressure increases, more complex equations are needed (Van der Waals, virial...)
 
* Expanded liquid
* Compressed liquid
* Solid
 
If the area is further reduced once the solid phase has been reached, collapse occurs, the monolayer breaks and soluble aggregates and multilayers are formed
 
Gibbs monolayers also follow equations of state, which can be deduced from [[Gibbs isotherm]].
* For very dilute solutions <math>\gamma = \gamma_o - mC</math>, through Gibbs isotherm another analogous of ideal gas law is reached <math>\Pi = \Gamma R T</math>
* For more concentrated solutions and applying Langmuir isotherm <math>\Gamma = \Gamma_{\max} \frac{C}{a+C}</math>, thus <math>\Pi = \Gamma_{\max}RT \left(1+\frac{C}{a}\right)</math>
 
== Biology ==
Monolayers are frequently encountered in [[biology]]. A [[micelle]] is a monolayer, and the [[phospholipid]] [[lipid bilayer]] structure of [[cell membrane|biological membrane]]s is technically two monolayers.
 
=== Cell culture ===
In [[cell culture]] a monolayer refers to a layer of cells in which no cell is growing on top of another, but all are growing side by side and often touching each other on the same growth surface.
 
== See also ==
* [[Self-assembled monolayer]]
 
==References==
<references/>
 
==External links==
* {{cite web |url=http://goldbook.iupac.org/M04015.html |title=Monolayer |work=Goldbook |publisher=[[IUPAC]] |accessdate=November 5, 2012}}
 
[[Category:Phases of matter]]
[[Category:Thin films]]
[[Category:Physical chemistry]]

Revision as of 05:24, 28 February 2014

I'm a 30 years old and working at the university (Neuroscience).
In my spare time I'm trying to teach myself Swedish. I've been there and look forward to go there sometime near future. I like to read, preferably on my kindle. I really love to watch The Vampire Diaries and Game of Thrones as well as docus about anything astronomical. I enjoy Art collecting.

Feel free to surf to my website; Fifa 15 Coin Generator; Gesinvalles.Es,