Thermal Desorption using Transition State Theory

Minissale+ 2022 proposes that a nontrivial determination of the pre-exponential factor, ν \nu using transition state theory can affect the binding energy value E E .

Previous Thermal Desorption equation

It is found experimentally that ln⁡(k) \ln (k) (where k k is the rate) of many processes involving atoms and molecules (reactions, desorption, diffusion) gives a straight line when plotted against 1/T 1 / T . This behavior is usually described by the Arrhenius equation:

k=νexp⁡(−EakBT) k=\nu \exp \left(-\frac{E_{\mathrm{a}}}{k_{\mathrm{B}} T}\right)

Usually, the following equation for the characteristic frequency (Tielens and Allamandola 1987) is assumed:

ν=2NsEbind, Aπ2mA \nu = \sqrt{\frac{2 N_s E_{\text {bind, } \mathrm{A}}}{\pi^2 m_A}}

However, several experimental works have pointed out that bigger molecules may exhibit prefactor values several orders of magnitude higher than what is predicted by the previous formula, sometimes reaching 1020 s−110^{20} \mathrm{~s}^{-1}.

Minissale's Approach

In the transition state theory (TST), it can be written as

νTST=kBThq‡qads \nu_{\mathrm{TST}} = \frac{k_{\mathrm{B}} T}{h} \frac{q^{\ddagger}}{q_{\mathrm{ads}}}

Now that the recommended ν\nu has been estimated through the transition state theory (TST), while by equalizing the desorption fluxes of the given species at Tpeak T_{\text {peak }} :

νTSTe−Eb/(kbTpeak)=νLVe−ELV/(kbTpeak) \nu_{\mathrm{TST}} \mathrm{e}^{-E_{\mathrm{b}} /\left(k_b T_{\text{peak}}\right)} = \nu_{\mathrm{LV}} \mathrm{e}^{-E_{\mathrm{LV}} /\left(k_b T_{\text{peak}}\right)}

we can calculate the recommended EbE_{\mathrm{b}} using

Eb=ELV−Tpeakln⁡(νLV/ν) E_{\mathrm{b}} = E_{\mathrm{LV}} - T_{\text{peak}} \ln \left(\nu_{\mathrm{LV}} / \nu\right)

where ELVE_{\mathrm{LV}} and νLV\nu_{\mathrm{LV}} are the desorption parameters chosen from literature and Tpeak T_{\text {peak }} is the temperature at which the maximum desorption rate for a 1 ML TPD is found for a given species.

Minissale's Table

Minissale critically assesses the desorption parameters (the binding energies, EbE_b, and the pre-exponential factor, ν\nu) commonly used in the astrochemical community and provides tables with recommended values.

The objective of the tables is to list the existing experimental and theoretical values on the different surfaces and in the submonolayer regime, showing the disparity of the studies, and then to propose a single value, a simplified version recommended to those who would like to use a single value in the framework of a more complicated astrophysical model.

Index Spec Freq_ads E_D(K) Peak Temp Surface
0 H₂ 1.980000e+11 371 20 ASW
1 H 1.540000e+11 450 15 ASW
2 N 1.170000e+13 806 35 ASW
3 N₂ 4.510000e+14 1074 35 ASW
4 O₂ 5.980000e+14 1107 35 ASW
5 CH₄ 5.430000e+13 1232 47 ASW
6 CO 9.140000e+14 1390 35 ASW
7 O 2.730000e+13 1751 50 ASW
8 C₂H₂ 4.990000e+15 2877 70 ASW
9 CO₂ 6.810000e+16 3196 80 ASW
10 H₂S 4.950000e+15 3426 85 ASW
11 H₂CO 8.290000e+16 4117 95 ASW
12 CS 6.650000e+16 4199 90 ASW
13 HCN 1.630000e+17 5344 137 ASW
14 NH₃ 1.940000e+15 5362 105 ASW
15 OH 3.760000e+15 5698 140 ASW
16 H₂O 4.960000e+15 5705 155 ASW
17 CH₃CN 2.370000e+17 6253 120 ASW
18 CH₃OH 3.180000e+17 6621 128 ASW
19 NH₂CHO 3.690000e+18 9561 176 ASW
20 C 7.380000e+14 15981 300 ASW

Step 1

To use Minissale's new value, a file named AdsorptionEnergies_Minissale.in should be in the same folder as Parameter.in. The contents of AdsorptionEnergies_Minissale.in look like the table above on the page. The incorporation of pre-exponential factor ν\nu largely follows the previous way of treating EadsE_{\text{ads}} as elaborated in Eads.

Step 2

Include the two lines in Parameter.in. Eads_Minissale is the new flag just added.

.true.      ! Eads_from_file      : from AdsorptionEnergies.in
.true.      ! Eads_Minissale      : use Minissale et al. 2016 adsorption energies and frequencies