Mono time

Physical experiments to determine the properties of the surface of solids require particularly clean conditions; even a monolayer can lead to incorrect results. In practice, the term mono time t _{mono has become} widespread. This is a measure of the time in which the surface of the solid has not yet been significantly contaminated by molecules of the residual gas that is inevitably present in the vacuum chamber . It thus describes the working time available to obtain useful results. The mono time is defined as the period in which a previously pure solid surface is covered with a monolayer due to residual gas deposition.

The definition of mono time is based on the assumption that every particle hitting the surface is adsorbed with a probability of 1, i.e. that it remains adhered in any case. The relationship applies to the deposition of a monolayer n _mono

${\displaystyle j_{\mathrm {ad} }\cdot t_{\mathrm {mono} }=n_{\mathrm {mono} }}$.

Here, j _{ad is} the area-related adsorption rate and is proportional to the number of particles n as well as to the average speed of the precipitating molecules, cf. Maxwell-Boltzmann distribution . The mono time is therefore dependent on the temperature T and the pressure p prevailing in the system , the relationship applies ${\displaystyle {\overline {v}}}$

${\displaystyle t_{\mathrm {mono} }\propto {\frac {\sqrt {T}}{p}}}$

In addition, the mono time is of course a material-specific parameter, depending on the combination of adsorbent (surface) and adsorbate (residual gas). With the general gas constant R , the particle density n _mono , the molar mass M _molar (see molar mass ) and the Avogadro number N _A :

${\displaystyle t_{\mathrm {mono} }={\frac {n_{\mathrm {mono} }}{p\cdot N_{A}}}{\sqrt {2\pi M_{\mathrm {molar} }RT}}}$

How clearly the pressure dependency appears can be seen in the following numerical example of typical mono times: At a pressure of 10 ⁻⁶  mbar, one monolayer per second is deposited on the order of magnitude; in an ultra-high vacuum at 10 ⁻¹¹  mbar, the mono time is already in the range of 24 hours.