Monolayer

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:

${\displaystyle t={\frac {3\times 10^{-4}\,\mathrm {Pa} \cdot \mathrm {s} }{P}}}$

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 μPa (2×10⁻⁶ Torr).

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 (${\displaystyle \Pi =\gamma ^{o}-\gamma }$, where ${\displaystyle \gamma ^{o}}$ is the surface tension of the interface before the monolayer is formed) with the area (the inverse of surface concentration ${\displaystyle \Gamma ^{-1}}$). It is analogous with a 3D process in which pressure varies with volume.

A variety of bidimensional 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 equations of state for 3D gases can be used: ideal gas law ${\displaystyle \Pi A=RT}$, where ${\displaystyle A}$ 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 ${\displaystyle \gamma =\gamma _{o}-mC}$, through Gibbs isotherm another analogous of ideal gas law is reached ${\displaystyle \Pi =\Gamma RT}$
• For more concentrated solutions and applying Langmuir isotherm ${\displaystyle \Gamma =\Gamma _{\max }{\frac {C}{a+C}}}$, thus ${\displaystyle \Pi =\Gamma _{\max }RT\left(1+{\frac {C}{a}}\right)}$