Editing Monolayer (section)

=== 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>