Editing Desorption (section)

== Mechanisms ==
Depending on the nature of the adsorbent-to-surface bond, there are a multitude of mechanisms for desorption. The surface bond of a sorbant can be cleaved thermally, through chemical reactions or by radiation, all which may result in desorption of the species.

=== 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>

=== Reductive or oxidative desorption ===
In some cases, the adsorbed molecule is chemically bonded to the surface/material, providing a strong adhesion and limiting desorption. If this is the case, desorption requires a chemical reaction which cleaves the [[chemical bond]]s. One way to accomplish this is to apply a voltage to the surface, resulting in either reduction or oxidation of the adsorbed molecule (depending on the bias and the adsorbed molecules).

In a typical example of reductive desorption, a [[self-assembled monolayer]] of [[thiol|alkyl thiols]] on a [[gold]] surface can be removed by applying a negative bias to the surface resulting in reduction of the sulfur head-group. The chemical reaction for this process would be:

: <math>R - S - Au + e^- \longrightarrow R - S^- + Au </math>

where R is an alkyl chain (e.g. CH<sub>3</sub>), S is the sulfur atom of the thiol group, Au is a gold surface atom and e<sup>−</sup> is an electron supplied by an external voltage source.<ref>Sun, K., Jiang, B., & Jiang, X. (2011). Electrochemical desorption of self-assembled monolayers and its applications in surface chemistry and cell biology. ''Journal of Electroanalytical Chemistry'', ''656''(1), 223-230.</ref>

Another application for reductive/oxidative desorption is to clean active carbon material through [[electrochemical regeneration]].

===Electron-stimulated desorption===
[[File:Electron Stimulated Desorption Video.webm|thumb|shows the effects of an incident electron beam on adsorbed molecules]]
Electron-stimulated desorption occurs as a result of an electron beam incident upon a surface in vacuum, as is common in [[particle physics]] and industrial processes such as scanning electron microscopy (SEM). At atmospheric pressure, molecules may weakly bond to surfaces in what is known as [[adsorption]]. These molecules may form monolayers at a density of 10<sup>15</sup> atoms/cm<sup>2</sup> for a perfectly smooth surface,.<ref>M. H. Hablanian (1997). ''High-Volume Technology, A Practical Guide''. Second Edition. Marcel Dekker, Inc.</ref>  One monolayer or several may form, depending on the bonding capabilities of the molecules.  If an electron beam is incident upon the surface, it provides energy to break the bonds of the surface with molecules in the adsorbed monolayer(s), causing pressure to increase in the system. Once a molecule is desorbed into the vacuum volume, it is removed via the vacuum's pumping mechanism (re-adsorption is negligible).  Hence, fewer molecules are available for desorption, and an increasing number of electrons are required to maintain constant desorption.

One of the leading models on electron stimulated desorption is described by Peter Antoniewicz<ref name="peter">
Model for electron- and photon-stimulated desorption, Antoniewicz, Peter R., Phys. Rev. B 21.9, pages: 3811—3815, May 1980, American Physical Society, doi = {10.1103/PhysRevB.21.3811},</ref> In short, his theory is that the adsorbate becomes ionized by the incident electrons and then the ion experiences an image charge potential which attracts it towards the surface. As the ion moves closer to the surface, the possibility of electron tunnelling from the substrate increases and through this process ion neutralisation can occur. The neutralised ion still has kinetic energy from before, and if this energy plus the gained potential energy is greater than the binding energy then the ion can desorb from the surface. As ionisation is required for this process, this suggests the atom cannot desorb at low excitation energies, which agrees with experimental data on electron simulated desorption.<ref name="peter" /> Understanding electron stimulated desorption is crucial for accelerators such as the [[Large Hadron Collider]], where surfaces are subjected to an intense bombardment of energetic electrons. In particular, in the beam vacuum systems the desorption of gases can strongly impact the accelerators performance by modifying the secondary electron yield of the surfaces.<ref>Electron Stimulated Desorption of Condensed Gases on Cryogenic Surfaces (September 2005) Dipl. Ing. Herbert Tratnik Matrikelnr. 9226169, page:3 </ref>

===IR photodesorption===
IR photodesorption is a type of desorption that occurs when an infrared light hits a surface and activates processes involving the excitation of an internal vibrational mode of the previously absorbed molecules followed by the desorption of the species into the gas phase.<ref name="Hussla">PHYSICAL REVIEW 8, volume 32, number 615. September 1985. Infrared-laser-induced photodesorption of NH3 and ND3 adsorbed single crystal Cu(100) and Ag film. IngoHussla, H.Seki, T.J.Chuang. IBMResearchLaboratory, SanJose, California.</ref> One can selectively excite electrons or vibrations of the adsorbate or of the adsorbate-substrate coupled system. This relaxation of the bonds together with a sufficient energy exchange from the incident light to the system will eventually lead to desorption.<ref name="Brivio">Surface Science Reports 17 (1993) 1-84 North-Holland. Dynamics of adsorption/desorption at solid surfaces G.P. Brivio a and T.B. Grimley b,1 Dipartimento di Fisica dell'Universith di Milano, Via Celoria 16, 20133 Milano, Italy h The Donnan Laboratories, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK Manuscript received in final form 25 August 1992  </ref> 

Generally, the phenomenon is more effective for weaker-bound physisorbed species, which have a smaller adsorption potential depth compared to that of the chemisorbed ones. In fact, a shallower potential requires lower laser intensities to set a molecule free from the surface and make IR-photodesorption experiments feasible, because the measured desorption times are usually longer than the inverse of the other relaxation rates in the problem.<ref name="Brivio" />

===Phonon activated desorption===
In 2005, a mode of desorption was discovered by John Weaver et al. that has elements of both thermal and electron stimulated desorption. This mode is of particular interest as desorption can occur in a closed system without external stimulus.<ref> Physics Today 58, 5, 9 (2005); doi: 10.1063/1.1995718</ref> The mode was discovered whilst investigating bromine absorbed on silicone using [[scanning tunneling microscope|scanning tunnelling microscopy]]. In the experiment, the Si-Br wafers were heated to temperatures ranging from 620 to 775 K.<ref>Electron-stimulated desorption from an unexpected source: Internal hot electrons for Br–Si(1 0 0)-(2 · 1) B.R. Trenhaile, V.N. Antonov, G.J. Xu, Koji S. Nakayama, J.H. Weaver * Department of Physics, Department of Materials Science and Engineering, and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States Received 14 February 2005; accepted for publication</ref> However, it was not simple thermal desorption bond breaking that was observed as the activation energies calculated from [[Arrhenius plot|Arrhenius plots]] were found to be lower than the Si-Br bond strength. Instead, the optical phonons of the Silicon weaken the surface bond through vibrations and also provide the energy for electron to excite to the [[antibonding molecular orbital|antibonding]] state.