Pfeiffer Vacuum A Passion for Perfection

1.3.3 Desorption, diffusion, permeation and leaks

In addition to water, other substances (oil) can be adsorbed on surfaces. Substances can also diffuse out of the metal walls, which can be evidenced in the residual gas. In the case of particularly rigorous requirements, stainless steel vessels can be baked out under vacuum, thus driving the majority of the volatile components out of the metal walls.


Gas molecules, (primarily water) are bound to the interior surfaces of the vacuum chamber through adsorption and absorption, and gradually desorb again under vacuum. The desorption rate of the metal and glass surfaces in the vacuum system produces a gas yield that is a function of time, however. A good approximation can be obtained by assuming that after a given point in time t > t0 the reduction will occur on a linear basis over time. t0 is typically assumed to be one hour.

The gas yield can thus be described as:

Formula 1-24:


In this formula, qdes is the surface-based desorption rate of the material, A the interior surface area of the vacuum chamber, t0 the start time and t the duration.

Figure 1.10: Saturation vapor pressure of water
Source: Jousten (publisher) Wutz, Handbuch Vakuumtechnik, Vieweg Verlag

Diffusion with desorption

At operation below 10-6 mbar, desorption of plastic surfaces, particularly the seals, assumes greater significance. Plastics mainly give off the gases that are dissolved in these plastics, which first must diffuse on the surface.

Following extended pump downtimes, desorption from plastics can therefore dominate the metal surfaces. Although the surface areas of the seals are relatively small; the decrease in the desorption rate over time occurs more slowly in the case of metal surfaces. As an approximation it can be assumed that the reduction over time will occur at the square root of the time.

The gas produced from plastic surfaces can thus be described as:

Formula 1-25:

Desorption from plastic material

where Ad denotes the surface area of the plastics in the vacuum chamber and qdiff denotes the surface area-specific desorption rate for the respective plastic. At even lower pressures, similar effects also occur with metals, from which hydrogen and carbon escape in the form of CO and CO2 and can be seen in the residual gas spectrum. Formula 1-25 also applies in this regard.

Permeation and leaks

Seals, and even metal walls, can be penetrated by small gas molecules, such as helium, through diffusion. Since this process is not a function of time, it results in a sustained increase in the desired ultimate pressure. The permeation gas flow is proportional to the pressure gradient p0 /d (d = wall thickness, p0 = atmospheric pressure = ambient pressure) and to the permeation constants for the various materials kperm.

Formula 1-26:


Permeation first manifests itself at pressures below 10-8 mbar. Ql denotes the leakage rate, i.e. a gas flow that enters the vacuum system through leaks at a volume of V. The leakage rate is defined as the pressure rise Δp over time Δt:

Formula 1-27:

Leakage rate

If a vessel is continuously pumped out at a volume flow rate S, an equilibrium pressure pgl will be produced. Throughput Formula 1-13 is equal to the leakage rate Ql = S · pgl. A system is considered to be adequately tight if the equilibrium pressure pgl is approximately 10 % of the working pressure. If, for example, a working pressure of 10-6 mbar mbar is attained and the vacuum pump that is being used has a pumping speed of 100 l / s, the leakage rate should not be more than 10-5 mbar l / s. This corresponds to a leak of approximately 20 · 20 µm2 in size. Leakage rates Ql of less than 10-8 mbar l / s can usually be easily attained in clean stainless steel vessels. The ultimate pressure achievable after a given period of time t primarily depends upon all of the effects described above and upon the pumping speed of the vacuum pump. The prerequisite is naturally that the ultimate pressure will be high relative to the base pressure of the vacuum pump.

The specific pressure components for a given pumping time t can be calculated by using

Formula 1-28:

Ultimate pressure (t)

and by solving the equations for t. The achievable ultimate pressure is the sum of these pressures.

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