Editing Desorption (section)

=== Thermal desorption ===
Thermal desorption is the process by which an adsorbate is heated and this induces desorption of atoms or molecules from the surface. The first use of thermal desorption was by [[LeRoy Apker]] in 1948.<ref>L. Apker, Ind. Eng. Chem. 40 (1948) 846</ref> It is one of the most frequently used modes of desorption, and can be used to determine surface coverages of adsorbates and to evaluate the [[activation energy]] of desorption.<ref name="foo"> THERMAL DESORPTION ANALYSIS: COMPARATIVE TEST OF TEN COMMONLY APPLIED PROCEDURES A.M. de JONG and J.W. NIEMANTSVERDRIET * Laboratory of Inorganic Chemistry and Catalysis, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands Received 8 January 1990</ref>

Thermal desorption is typically described by the Polanyi-Wigner equation:

: <math>r(\theta) = - \frac{\text{d}\theta}{\text{d}t} = \upsilon(\theta) \theta^n \exp\left(\frac{-E(\theta)}{RT}\right)</math>

where ''r'' is the rate of desorption, <math>\theta</math> is the adsorbate coverage, ''t'' the time, ''n'' is the order of desorption, <math>\upsilon</math> the [[pre-exponential factor]], ''E'' is the activation energy, ''R'' is the [[gas constant]] and T is the absolute temperature. The adsorbate coverage is defined as the ratio between occupied and available adsorption sites.<ref name="foo" />

The order of desorption, also known as the kinetic order, describes the relationship between the adsorbate coverage and the rate of desorption. In first order desorption, {{nobr|n {{=}} 1}}, the rate of the particles is directly proportional to adsorbate coverage.<ref name="basic" /> Atomic or simple molecular desorption tend to be of the first order and in this case the temperature at which maximum desorption occurs is independent of initial adsorbate coverage. Whereas, in second order desorption the temperature of maximum rate of desorption decreases with increased initial adsorbate coverage. This is because second order is re-combinative desorption and with a larger initial coverage there is a higher probability the two particles will find each other and recombine into the desorption product. An example of second order desorption, {{nobr|n {{=}} 2}}, is when two hydrogen atoms on the surface desorb and form a gaseous {{chem|H|2}} molecule.  There is also zeroth order desorption which commonly occurs on thick molecular layers, in this case the desorption rate does not depend on the particle concentration. In the case of zeroth order, {{nobr|n {{=}} 0}}, the desorption will continue to increase with temperature until a sudden drop once all the molecules have been desorbed.<ref name="basic" /> 

In a typical thermal desorption experiment, one would often assume a constant heating of the sample, and so temperature will increase linearly with time. The rate of heating can be represented by
: <math>\beta = \frac{\mathrm{d}T}{\mathrm{d}t}</math>

Therefore, the temperature can be represented by: 
: <math>T(t) = \beta(t - t_0) + T_0</math>

where <math> t_0 </math> is the starting time and <math> T_0 </math> is the initial temperature.<ref name="basic">BASIC TECHNIQUES OF SURFACE PHYSICS Surface Analysis with Temperature Programmed Desorption and Low-Energy Electron Diffraction, Versuch Nr. 89 F-Praktikum in den Bachelor- und Masterstudiengängen, SS2017 Physik Department Lehrstuhl E20, Raum 205 Contacts: Dr. Y.-Q. Zhang, Dr. T. Lin and Dr. habil. F. Allegretti</ref> At the "desorption temperature", there is sufficient thermal energy for the molecules to escape the surface. One can use the thermal desorption as a technique to investigate the binding energy of a metal.<ref name="basic" />

There are several different procedures for performing analysis of thermal desorption. For example, Redhead's peak maximum method<ref name = "redhead">Redhead, P.A. (1962). "Thermal desorption of gases". Vacuum. 12 (4): 203–211. Bibcode:1962Vacuu..12..203R. doi:10.1016/0042-207X(62)90978-8</ref> is one of the ways to determine the activation energy in desorption experiments. For first order desorption, the activation energy is estimated from the temperature (''T''<sub>''p''</sub>) at which the desorption rate is a maximum. Using the equation for rate of desorption (Polyani Winer equation), one can find ''T''<sub>''p''</sub>, and Redhead shows that the relationship between ''T''<sub>''p''</sub> and ''E'' can be approximated to be linear, given that the ratio of the rate constant to the heating rate is within the range 10{{sup|8}} – 10{{sup|13}}. By varying the heating rate, and then plotting a graph of <math>\log(\beta)</math> against <math>\log(T_p)</math>, one can find the activation energy using the following equation: 
: <math>\frac{\mathrm{d}\log(\beta)}{\mathrm{d}\log(T_p)} = \frac{E}{RT_p} + 2 </math><ref name = "redhead"/>

This method is straightforward, routinely applied and can give a value for activation energy within an error of 30%. However a drawback of this method, is that the rate constant in the Polanyi-Wigner equation and the activation energy are assumed to be independent of the surface coverage.<ref name = "redhead"/>

Due to improvement in computational power, there are now several ways to perform thermal desorption analysis without assuming independence of the rate constant and activation energy.<ref name="foo" /> For example, the "complete analysis" method<ref>King, David A. (1975). "Thermal desorption from metal surfaces: A review". Surface Science. 47 (1): 384–402. Bibcode:1975SurSc..47..384K. doi:10.1016/0039-6028(75)90302-7.</ref> uses a family of desorption curves for several different surface coverages and integrates to obtain coverage as a function of temperature. Next, the desorption rate for a particular coverage is determined from each curve and an [[Arrhenius plot]] of the logarithm of the rate of desorption against 1/T is made. An example of an Arrhenius plot can be seen in the figure on the right. The activation energy can be found from the gradient of this [[Arrhenius plot]].<ref name=thesis>Zaki, E. (2019). Surface-Sensitive Adsorption of Water and Carbon Dioxide on Magnetite: Fe3O4(111) versus Fe3O4(001). PhD Thesis, Technische Universität, Berlin.</ref>

[[File:N-pentane desorption from pellets of NaX zeolite (mdpi - 3662).png|thumb|Theoretical processing of the experimental data on n-pentane desorption from pellets of NaX zeolite]]
It also became possible to account for an effect of the disorder on the value of activation energy ''E'', that leads to a non-Debye desorption kinetics at large times and allows to explain both desorption from close-to-perfect silicon surfaces and desorption from microporous adsorbents like ''NaX'' [[Zeolite|zeolites]]. <ref>{{cite journal |last1=Bondarev |first1=V |last2=Kutarov |first2=V |last3=Schieferstein |first3=E |last4=Zavalniuk |first4=V |name-list-style=amp |title=Long-Time Non-Debye Kinetics of Molecular Desorption from Substrates with Frozen Disorder | journal=Molecules |year=2020 |volume=25 |issue=16 |pages=3662(14) |doi=10.3390/molecules25163662 |pmid=32796720 |pmc=7464774 |doi-access=free }}</ref>

[[File:Arrhenius.svg|thumb|right|An example of an Arrhenius plot, with the natural logarithm of the rate of reaction (k) plotted against one over the temperature.]]
Another analysis technique involves simulating thermal desorption spectra and comparing to experimental data. This technique relies on kinetic [[Monte Carlo method|Monte Carlo simulations]] and requires an understanding of the lattice interactions of the adsorbed atoms. These interactions are described from first principles by the Lattice Gas Hamiltonian, which varies depending on the arrangement of the atoms. An example of this method used to investigate the desorption of oxygen from rhodium can be found in the following paper: "Kinetic Monte Carlo simulations of temperature programed desorption of O/Rh(111)".<ref>Kinetic Monte Carlo simulations of temperature programed desorption of O/Rh(111) J. Chem. Phys. 132, 194701 (2010) T. Franza and F. Mittendorfer</ref>