Impingement rate, monolayer time, and Langmuir exposure

The impingement rate Z (molecular flux) quantifies how many gas molecules strike a unit area of surface per unit time. From kinetic theory, for an ideal gas one finds Z = P / √(2πmk_B T), where P is pressure, m molecular mass, k_B Boltzmann's constant, and T temperature. When expressed in convenient vacuum units (P in Torr, T in K, M in g/mol), this is often written as:

Z ≈ 3.5 × 10²² · P[Torr] / √(M · T) molecules/(cm²·s)

A common engineering estimate for a monolayer on a surface is N_ML ≈ 10¹⁵ molecules/cm². For a sticking coefficient s, the effective flux that actually adheres is Z·s, and the characteristic monolayer formation time is t_ML ≈ N_ML / (Z·s). At 10⁻⁶ Torr with s ≈ 1, t_ML is on the order of 1 second, illustrating how quickly surfaces can become contaminated even at "good" vacuum.

The Langmuir is a traditional unit of exposure defined as 1 L = 10⁻⁶ Torr·s. For many adsorption systems, an exposure of order 1 L with s ≈ 1 corresponds roughly to a monolayer. At fixed pressure, the time to accumulate one Langmuir is t_1L ≈ 10⁻⁶ / P[Torr]. For example, at 10⁻⁷ Torr, t_1L ≈ 10 seconds.

Our Impingement / Monolayer / Langmuir tool implements these relationships. Given pressure, temperature, molar mass, and an assumed sticking coefficient, it reports Z, monolayer formation time, Langmuir exposure for a chosen time, and the time required to reach 1 L at that pressure.