TPD Calculator for a Lattice Gas

This page can simulate temperature programmed desorption (TPD) spectra. It can also calculate the adsorption energy distribution from an experimental TPD spectrum at saturation coverage.
For more information and the underlying theory, see M. Schmid, G. S. Parkinson, U. Diebold, Analysis of temperature-programmed desorption via equilibrium thermodynamics, ACS Phys. Chem. Au 2 (2022).
Currently this page does not include the “magic formula”, which determines the adsorption energy from the peak temperature and peak width. When the peak temperature is given, this calculator performs a TPD simulation based on the input data. You can then check whether the peak width agrees with experiment. If it doesn't, the assumptions made in the input (sticking coefficient, soft vibration modes, dissociation for molecules like H₂, single adsorption energy vs. energy distribution, etc.) need to be questioned. When doing a simulation for a single adsorption energy, this page provides some thermodynamic data required for the magic formula (gray output below the input fields).

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Calculation for what	E_ads given T_peak given Distribution of E_ads given TPD curve given, get E_ads distrib.		Calculate Wait (calculating)...
Units	J/mol eV
Gas		a)   dissociates
Atom types, x, y, z	C 0 0 0 O 0 0 1.13		units m
Ramp rate β		K/s
Adsorption sites/area na		m⁻² cm⁻² nm⁻²
Tpeak		K; FWHM = K
|Eads0|		J/mol   b)
|Eads0|, fraction	1e5,1		J/mol   b)
Adsorbate vibrations Evib			cm-1   c)
Extra entropy Sad,extra/R			d)
Initial coverage θ0
Multiple coverages			e)
Sticking:    Constant: s		(mobile precursor)
Per free site: s0		(Langmuir-type adsorption)
Formula: s(θ, T)			f)

 

Plot experimental Experimental TPD curve(s) for comparison: T (K), rate, [T, ] rate...
Ionization probability correction (√T) ^g)
230,0.01 232,0.04 234,0.08 236,0.16 238,0.32 240,0.50 242,0.62 244,0.76 246,0.93 248,1.14 250,1.38 252,1.68 254,2.03 256,2.46 258,2.95 260,3.54 262,4.24 264,5.05 266,6.00 268,7.11 270,8.41 272,9.90 274,11.63 276,13.61 278,15.88 280,18.46 282,21.39 284,24.69 286,28.40 288,32.52 290,37.08 292,42.08 294,47.50 296,53.32 298,59.48 300,65.87 302,72.38 304,78.81 306,84.91 308,90.38 310,94.82 312,97.80 314,98.81 316,97.33 318,92.92 320,85.27 322,74.41 324,60.83 326,45.67 328,30.65 330,17.74 332,8.46 334,3.15 336,0.85 338,0.15 340,0.02

Expert mode: Number of sharpening iterations Noise suppression (0–10) ^h)
Output: |E_ads⁰| (J/mol), fraction, θ, ρ(|E_ads⁰|), ρ_raw(|E_ads⁰|), θ(T), T
 

^a) For the predefined gases except H₂, data are inaccurate below 100 K. For lower temperatures, better select 'OTHER' and enter the molecular structure. Dissociation is only supported for molecules dissociating into two atoms of equal type (H₂, D₂, N₂, and O₂).
^b) E_ads⁰ is the adsorption energy for T = 0, i.e., without vibrational energies of the adsorbate. Energy per atom when dissociating. Each line should contain two numbers, |E_ads⁰|, f, where f is the fraction or relative number of adsorption sites with this adsorption energy. (You need not care about normalization; the program will normalize it such that the sum of all f values becomes unity.) |E_ads⁰| values must be given in ascending order. Further data columns will be ignored.
^c) Comma-separated list, leave empty if none. Enter all modes for the adsorbate if the gas is one of the pre-defined ones. For 'OTHER' gases, omit vibration modes that are equal for the gas phase and the adsorbed molecule. Enter vibration modes present only in the adsorbed molecules as positive numbers and modes present only in the gas phase as negative numbers. Modes with high E_vib = hν (above a few k_BT) can be ignored.
^d) Adsorbate entropy not related to site occupation and vibrations, divided by R. E.g., ln(3) for three distinguishable azimuthal orientations. See ^f) for how to enter a formula.
^e) Enter the step Δθ₀, or a list of initial coverages θ₀₍₁₎, θ₀₍₂₎,... (best in descending sequence). These coverages should be less than the θ₀ value of the main calculation.
^f) Variables: θ or th, T, and s (output; optional if a simple expression is given). Declare own variables with var. Predefined constants h (Planck), k (Boltzmann), R (gas), and e (elementary charge, eV/J). Functions: sqrt, sqr, ln or log, exp, pow(base, exponent), and JavaScript Math functions. Examples: sqr(1-θ) or var x=10*(1-th); s=x/(1+x).
^g) Assumes that the ionization probability in the mass spectrometer is inversely proportional to the velocity, which is proportional to √T. This correction should be applied only if the desorbing molecules directly enter the mass spectrometer, without being reflected at any surfaces. The correction is also inaccurate in case of a barrier on adsorption, causing temperature-dependent sticking.
^h) Select 'Expert mode' to control the fitting process used for determination of the energy distribution (Richardson–Lucy method). The raw energy distribution is iteratively refined to better fit the experimental data. A high number of iterations (default 50) can lead to a better fit, but takes more computing time and may also result in isolated desorption energies even in case of a continuous distribution of energies, to better fit the experimental noise. If you get at least one rather sharp peak in the energy distribution and the calculated TPD peak corresponding to it is not as sharp as the experimental one, consider increasing the number of iterations. The noise suppression (default value 5) reduces sharpening broad distributions of the adsorption energy.
In expert mode, the energy distribution plot contains additional information: The raw correction factor is the ratio of experimental and calculated peak intensity in the last iteration of the Richardson–Lucy refinement, and the correction factor actually applied is obtained by smoothing this raw factor. The plot also shows the raw energy distribution ρ_raw and an intermediate result for ρ(|E_ads⁰|), to visualize how it evolves from ρ_raw to the final result.  Hide footnotes

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T, Calculated desorption rate(s)
 

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Author: Michael Schmid, IAP/TU Wien.
This work is licensed under GNU General Public License (GPLv3) and Creative Commons Attribution-ShareAlike 4.0 (CC-BY-SA 4.0). The plot library Plotly is licensed under the MIT license.
When using and/or modifying this program for scientific work please cite our paper:
Michael Schmid, Gareth S. Parkinson, and Ulrike Diebold, Analysis of temperature-programmed desorption via equilibrium thermodynamics ACS Phys. Chem. Au (2022), doi: 10.1021/acsphyschemau.2c00031.
For offline use, the latest version of this program (updated with respect to the one in this paper) is available via the download page.
Note that exporting the plot as .png file may not work correctly in Firefox if privacy.resistFingerprinting is enabled in about:config.