Electron Impact Reaction
The Electron Impact Reaction node () sets up the reaction rate for a reaction involving an electron and a target species.
Reaction Formula
Enter chemical reaction formulas in the Formula text field. The physics interface examines the species taking part in the reaction and automatically adds the associated Species features to the Model Builder.
Electron impact reactions are always assumed to be irreversible. However, the reverse reaction is automatically created if it is specified that a detailed balance should be constructed in the cross section data file. See Importing Collision Cross-Section Data.
Entering a Formula
The letter “e” is reserved to represent an electron. Therefore, if a formula such as e+Ar=>e+Ar+ is entered, the species e is automatically assigned as an electron.
Valid species names consist of a case-sensitive combination of letters, numbers, and “+” or “-” signs. With the exception of the “+” and “-” signs, which are used for ions, special characters are not allowed as species names or part of species names (for example, (), [], *, #, and _). In addition, the first character in a species name must be a letter to avoid confusion with the stoichiometric coefficients in the reaction formula. Ions are labeled with one plus or minus sign per species charge added directly after the species name. For example, O++ represents an oxygen atom with a twofold positive charge; O2+ represents molecular oxygen with a single positive charge; and 2O+ represents two oxygen atoms, each with a single positive charge. This labeling automatically fills in the charge of the species ion the Charge text field in the associated Species node.
Collision Type
This section is available when a valid formula for the electron impact reaction is entered.
Select a Collision type — Elastic (the default), Excitation, Attachment, or Ionization.
•
For Elastic enter a value for the Electron mass ratio mr (dimensionless) (the ratio of the mass of the electron to the target species).
•
Select Excitation for excitation reactions where the collision is inelastic. Enter the Energy loss Δe (SI unit: V) for the reaction. This is also known as threshold energy for the reaction. Select this option for electronic excitation, vibrational and rotational excitation, and superelastic collisions. For superelastic collisions, the activation energy is negative.
•
Select Attachment for collisions which result in the electron attaching to the target species, forming a negative ion. No user input is required.
•
Select Ionization for electron impact reactions which result in secondary electrons being formed. Enter the Energy loss Δe (SI unit: V) for the reaction. This is also known as threshold energy for the reaction.
Collision
This section is available when a valid formula for the electron impact reaction is entered.
Specify how to specify the reaction rate constant. There are these options:
•
For Cross section data enter cross-section data directly into a table for the electron impact reaction.
•
For Arrhenius parameters use Arrhenius coefficients to specify the reactions dependence on the electron “temperature”, Te.
•
For Rate constant specify an arbitrary expression for the rate constant. This can be a numeric value or a complicated function of the electron “temperature”, gas temperature, or any other expression. This is the default option for specifying the reaction.
•
For Use lookup table either enter or load in a lookup table of the source coefficient versus mean electron energy.
Cross Section Data
This section is available when a valid formula is entered for the electron impact reaction and the Specify reaction using option is set to Cross section data in the Collision section.
By default the electron energy distribution function is taken from the physics interface property. It can be changed to Maxwellian, Druyvesteyn, or Generalized. In this case, the selected distribution function is only used in the current electron impact reaction. The Electron energy in the Collision cross section data table should have units of electronvolts (eV). The units of the Collision cross section data has units of m2.
If a set of collision cross sections are loaded from a file with the Cross Section Import node, the software automatically generates the electron impact collisions and enters the cross section data into the Cross section data table.
Electron Energy Distribution Function Settings
Arrhenius Parameters
For Arrhenius parameters specify the reaction then COMSOL Multiphysics automatically generates an expression of the form
for the rate constant. Here, Af is the forward frequency factor, nf is the electron temperature exponent, and Ef is the activation energy (eV). The quantity Te is the electron “temperature” (eV), which is defined as
where is the mean electron energy.
Kinetic Expressions
If the Specify reaction using option is set to Rate constant then enter in an expression for the reaction forward rate constant in the Forward rate constant text field. The units of the rate constant depend on the order of the reaction.
Table 5-1: SI units for the rate constant for different reaction orders
order
example
SI unit
1
O2s=>O2
1/s
2
O+O2=>O3
m3/(s·mol)
3
3O=>O2+O
m6/(s·mol2)
Source Coefficient Data
If the Specify reaction using option is set to Use lookup table then the Source coefficient data section appears. Choose between Rate coefficients and Townsend coefficients to specify the source coefficients. For Rate coefficients either enter in the lookup table or load in from file a table of mean electron energy (eV) versus rate coefficient (SI unit: m3/s). For Townsend coefficients enter in or load data from file a table of mean electron energy (eV) versus Townsend coefficient (SI unit: m2).