Why We Bake — Mean Free Path

Why do we bake vacuum systems?

Every metal surface exposed to air adsorbs water, hydrocarbons, and atmospheric gases in multiple layers. At room temperature, these molecules cling to the surface for hours to years. Pumping alone cannot remove the most tightly bound layers.

Baking (heating to 120–250°C for 24–72 h) provides thermal energy that dramatically accelerates desorption. A surface at 150°C releases chemisorbed water 10⁹× faster than at room temperature. This is why bake-outs are essential for reaching UHV (<10⁻⁹ Torr).

r(T) = ν · exp(−E_a / k_BT)
Arrhenius desorption rate: ν = attempt frequency, E_a = activation energy, k_B = 8.617×10⁻⁵ eV/K

Molecular Surface Simulation

Watch molecules desorb from a metal surface as temperature rises. Each dot is a molecule bound with a specific energy. Drag the temperature slider below — at 150°C the water flies off; at 250°C+ only stubborn H₂ remains.

ON SURFACE 40 / 40

DESORPTION RATE 0.0 /s

THERMAL ENERGY 0.026 eV

H₂O physi (0.45 eV) H₂O chemi (0.90 eV) HC (0.60–1.0 eV) H₂ (0.40 eV) CO (1.10 eV)

Bake Race — 100°C vs 150°C

Two identical chambers. Same contamination. Different temperatures. Which one cleans first? Start the race and watch Arrhenius in action.

Chamber A:100°C Chamber B:150°C

Chamber A — 100°C

30 / 300 h

Race Time

0 h

Chamber B — 150°C

30 / 300 h

Chamber A

Chamber B

The Arrhenius equation is why vacuum scientists obsess over bake temperature. A 50°C increase doesn’t give you 50% more — it gives you 50× more. The energy cost of running the heaters hotter is trivial compared to the days of pumping time you save.

Temperature Simulator

Drag the slider to see how temperature affects outgassing. The bars show relative desorption rates for 8 species commonly found in accelerator vacuum systems.

TEMPERATURE

25 °C

Desorption Rate (H₂O chemi)

1.0s−1

Multiplier vs 25°C

1×

Mean Residence Time

--

Regime

Ambient

Arrhenius Rate vs Temperature

Logarithmic desorption rate for chemisorbed H₂O (E_a=0.9 eV). The vertical marker follows the slider. Notice how the rate changes by orders of magnitude over the bake temperature range.

Activation Energies & Parameters

Species	E_a (eV)	ν (s⁻¹)	Binding	Typical Source
H₂O physisorbed	0.45	10¹³	Van der Waals	Ambient humidity
H₂O chemisorbed	0.90	10¹³	Hydroxyl (OH)	Surface oxide layer
CO₂	0.50	10¹³	Weak chemisorption	Air exposure, decomposition
CO	1.10	10¹³	Metal-carbonyl	Oxide reduction, beam-induced
Light HC (C1–C3)	0.60	10¹³	Physisorbed	Pump oil, solvents
Heavy HC (C6+)	1.00	10¹³	Chemisorbed	Pump oil backstreaming
H₂ surface	0.40	10¹³	Physisorbed	Dissociative adsorption
H₂ bulk (diffusion)	0.50	10¹⁰	Interstitial	Dissolved in bulk steel

Key relationships:
Mean residence time: τ = 1/r(T) = (1/ν) · exp(E_a / k_BT)
Outgassing rate: q(T) ∝ n₀ · r(T) (monolayer model)
Diffusion-limited: q(T) ∝ D₀ · exp(−E_d/k_BT) / √t (bulk H₂)

References

[1] P.A. Redhead, J.P. Hobson, E.V. Kornelsen, The Physical Basis of Ultrahigh Vacuum, AIP, 1968.
[2] K. Jousten (ed.), Handbook of Vacuum Technology, 2nd ed., Wiley-VCH, 2016.
[3] M. Li & H.F. Dylla, "Model for the outgassing of water from metal surfaces," JVST A 11, 1702 (1993).
[4] C. Benvenuti, "Molecular surface pumping: the getter pump," CAS Vacuum Technology, CERN, 1999.
[5] SLAC-TN-23-003, "Vacuum bake-out procedures for LCLS-II cryomodules," 2023.