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| '''Physisorption''', also called '''physical adsorption''', is a process in which the electronic structure of the atom or molecule is barely perturbed upon [[adsorption]].<ref>{{citation|author=K. Oura et al.|title=Surface Science, An Introduction|location= Berlin|publisher= Springer|year= 2003| isbn =978-3-540-00545-2}}</ref><ref name=ConceptsinSurfacePhysics>{{citation |author=M. C. Desjonqueres et al |title=Concepts in surface physics |edition=2nd |url=http://books.google.com/?id=XW_Wvjwt5nIC&printsec=frontcover&dq=Concepts+in+surface+physics |place=New York |publisher=Springer-Verlag |date= 1996. Corrected printing 1998 |isbn=3-540-58622-9 |accessdate=29 August 2012}}</ref><ref>{{Citation|author=Hans Luth et al.|title=Surfaces and interfaces of solids|publisher= Springer-Verlag|year= 1993| isbn =978-3-540-56840-7}}</ref> | | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
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| ==Introduction==
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| The fundamental interacting force of physisorption is caused by [[van der Waals force]]. Even though the interaction energy is very weak (~10–100 meV), physisorption plays an important role in nature. For instance, the van der Waals attraction between surfaces and foot-hairs of [[gecko]]s provides the remarkable ability to climb up vertical walls.<ref>{{Citation | author=K. Autumn ''et al.''|title= Adhesive force of a single gecko foot-hair| journal=Nature| volume=405 | pages= 681–5| year=2000 | doi=10.1038/35015073 | pmid=10864324 | issue=6787}}</ref> Van der Waals forces originate from the interactions between induced, permanent or transient electric dipoles.
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| In comparison with [[chemisorption]], in which the electronic structure of bonding atoms or molecules is changed and covalent or ionic bonds form, physisorption, generally speaking, can only be observed in the environment of low temperature (thermal energy at room temperature ~26 meV) and the absence of the relatively strong chemisorptions. In practice, the categorisation of a particular adsorption as physisorption or chemisorption depends principally on the [[binding energy]] of the adsorbate to the substrate.
| | '''MathML''' |
| | :<math forcemathmode="mathml">E=mc^2</math> |
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| ==Modeling by image charge== | | <!--'''PNG''' (currently default in production) |
| [[Image:physisorption 1.jpg|thumbnail|200px|Fig. 1. Schematic illustration of an adsorbed hydrogen atom near a perfect [[electrical conductor|conductor]] interacting with its [[image charge]]s.]]
| | :<math forcemathmode="png">E=mc^2</math> |
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| To give a simple illustration of physisorption, we can first consider an adsorbed hydrogen atom in front of a perfect conductor, as shown in Fig. 1. A nucleus with positive charge is located at '''R''' = (0, 0, ''Z''), and the position coordinate of its electron, '''r''' = (''x'', ''y'', ''z'') is given with respect to the nucleus. The adsorption process can be viewed as the interaction between this hydrogen atom and its image charges of both the nucleus and electron in the conductor. As a result, the total electrostatic energy is the sum of attraction and repulsion terms:
| | '''source''' |
| | :<math forcemathmode="source">E=mc^2</math> --> |
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| :<math>V = {e^2\over 4\pi\varepsilon_0}\left(\frac{-1}{|2\mathbf R|}+\frac{-1}{|2\mathbf R+\mathbf r-\mathbf r'|}+\frac{1}{|2\mathbf R-\mathbf r'|}+\frac{1}{|2\mathbf R+\mathbf r|}\right).</math> | | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
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| The first term is the attractive interaction of nucleus and its image charge, and the second term is due to the interaction of the electron and its image charge. The repulsive interaction is shown in the third and fourth terms arising from the interaction of nucleus-image electron and electron-image nucleus, respectively.
| | ==Demos== |
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| By [[Taylor expansion]] in powers of |'''r'''| / |'''R'''|, this interaction energy can be further expressed as:
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
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| :<math>V = {-e^2\over 16\pi\varepsilon_0 Z^3}\left(\frac{x^2+y^2}{2}+z^2\right)+ {3e^2\over 32\pi\varepsilon_0 Z^4}\left(\frac{x^2+y^2}{2}{z}+z^3\right)+O\left(\frac{1}{Z^5}\right).</math>
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| One can find from the first non-vanishing term that the physisorption potential depends on the distance ''Z'' between adsorbed atom and surface as ''Z''<sup>−3</sup>, in contrast with the ''r''<sup>−6</sup> dependence of the molecular [[van der Waals]] potential, where ''r'' is the distance between two [[dipoles]].
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| ==Modeling by quantum-mechanical oscillator== | | ==Test pages == |
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| The [[van der Waals force|van der Waals]] binding energy can be analyzed by another simple physical picture: modeling the motion of an electron around its nucleus by a three-dimensional simple [[harmonic oscillator]] with a potential energy ''V<sub>a</sub>'':
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| :<math>V_a = \frac{m_e}{2}{\omega^2}(x^2+y^2+z^2),</math>
| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| | | *[[Url2Image|Url2Image (private Wikis only)]] |
| where ''m<sub>e</sub>'' and ''ω'' are the mass and vibrational frequency of the electron, respectively.
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| As this atom approaches the surface of a metal and forms adsorption, this potential energy ''V<sub>a</sub>'' will be modified due to the image charges by additional potential terms which are quadratic in the displacements:
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| :<math>V_a = \frac{m_e}{2}{\omega^2}(x^2+y^2+z^2)-{e^2\over 16\pi\varepsilon_0 Z^3}\left(\frac{x^2+y^2}{2}+z^2\right)+\ldots</math> (from the Taylor expansion above.)
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| Assuming
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| :<math> m_e \omega^2>>{e^2\over 16\pi\varepsilon_0 Z^3},</math>
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| the potential is well approximated as
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| :<math>V_a \sim \frac{m_e}{2}{\omega_1^2}(x^2+y^2)+\frac{m_e}{2}{\omega_2^2}z^2</math>,
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| where
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| :<math>
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| \begin{align}
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| \omega_1 &= \omega - {e^2\over 32\pi\varepsilon_0 m_e\omega Z^3},\\
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| \omega_2 &= \omega - {e^2\over 16\pi\varepsilon_0 m_e\omega Z^3}.
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| \end{align}
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| </math>
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| If one assumes that the electron is in the ground state, then the van der Waals binding energy is essentially the change of the zero-point energy:
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| :<math>V_v = \frac{\hbar}{2}(2\omega_1+\omega_2-3\omega)= - {\hbar e^2\over 16\pi\varepsilon_0 m_e\omega Z^3}.</math>
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| This expression also shows the nature of the ''Z''<sup>−3</sup> dependence of the van der Waals interaction.
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| Furthermore by introducing the atomic [[polarizability]],
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| :<math> \alpha= \frac {e^2} {m_e\omega^2},</math>
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| the van der Waals potential can be further simplified:
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| :<math>V_v = - {\hbar \alpha \omega\over 16\pi\varepsilon_0 Z^3}= -\frac{C_v}{Z^3},</math>
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| where
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| :<math>C_v = {\hbar \alpha \omega\over 16\pi\varepsilon_0},</math>
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| is the van der Waals constant which is related to the atomic polarizability.
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| Also, by expressing the fourth-order correction in the Taylor expansion above as (''aC<sub>v</sub>Z''<sub>0</sub>) / (Z<sup>4</sup>), where ''a'' is some constant, we can define ''Z''<sub>0</sub> as the position of the ''dynamical image plane'' and obtain
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| [[Image:physisorption table.jpg|thumbnail|400px|Table 1. The van der Waals constant ''C<sub>v</sub>'' and the position of the dynamical image plane ''Z''<sub>0</sub> for various rare gases atoms adsorbed on noble metal surfaces obtained by the jellium model. Note that ''C<sub>v</sub>'' is in eV/Å<sup>3</sup> and ''Z''<sub>0</sub> in Å.]] | |
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| :<math>V_v = - \frac{C_v}{(Z-Z_0)^3}+O\left(\frac{1}{Z^5}\right).</math>
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| The origin of ''Z''<sub>0</sub> comes from the spilling of the electron wavefunction out of the surface. As a result, the position of image plane representing the reference for the space coordinate is different from the substrate surface itself and modified by ''Z''<sub>0</sub>.
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| Table 1 shows the [[jellium]] model calculation for van der Waals constant ''C<sub>v</sub>'' and dynamical image plane ''Z''<sub>0</sub> of rare gas atoms on various metal surfaces. The increasing of ''C<sub>v</sub>'' from He to Xe for all metal substrates is caused by the larger atomic [[polarizability]] of the heavier rare gas atoms. For the position of the dynamical image plane, it decreases with increasing dielectric function and is typically on the order of 0.2 Å.
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| ==Physisorption potential== | |
| [[Image:physisorption 2.jpg|thumbnail|400px|Fig. 2. Calculated physisorption potential energy for He adsorbed on various [[jellium]] metal surfaces. Note that the weak van der Waals attraction forms shallow wells with energy about few meV.<ref name="Kohn"/>]] | |
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| Even though the [[van der Waals interaction]] is attractive, as the adsorbed atom moves closer to the surface the wavefunction of electron starts to overlap with that of the surface atoms. Further the energy of the system will increase due to the orthogonality of wavefunctions of the approaching atom and surface atoms.
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| This [[Pauli exclusion]] and repulsion are particularly strong for atoms with closed valence shells that dominate the surface interaction. As a result, the minimum energy of physisorption must be found by the balance between the long-range van der Waals attraction and short-range [[Pauli repulsion]]. For instance, by separating the total interaction of physisorption into two contributions- a short-range term depicted by [[Hartree–Fock]] theory and a long-range van der Waals attraction, the equilibrium position of physisorption for rare gases adsorbed on [[jellium]] substrate can be determined.<ref name="Kohn">{{Citation | author=E. Zaremba and W. Kohn|title= Theory of helium adsorption on simple and noble-metal surfaces| journal= Phys. Rev. B| volume=15 | issue=4 | pages= 1769| year=1977 | doi=10.1103/PhysRevB.15.1769|bibcode = 1977PhRvB..15.1769Z }}</ref> Fig. 2 shows the physisorption potential energy of He adsorbed on Ag, Cu, and Au substrates which are described by the [[jellium]] model with different densities of smear-out background positive charges. It can be found that the weak van der Waals interaction leads to shallow attractive energy wells (<10 meV). One of the experimental methods for exploring physisorption potential energy is the scattering process, for instance, inert gas atoms scattered from metal surfaces. Certain specific features of the interaction potential between scattered atoms and surface can be extracted by analyzing the experimentally determined angular distribution and cross sections of the scattered particles.
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| ==Comparison with chemisorption==
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| * Physisorption is a general phenomenon and occurs in any solid/fluid or solid/gas system. [[Chemisorption]] is characterized by chemical specificity.
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| * In physisorption, perturbation of the electronic states of adsorbent and adsorbate is minimal. For chemisorption, changes in the electronic states may be detectable by suitable physical means.
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| * Typical binding energy of physisorption is about 10–100 meV. Chemisorption usually forms bonding with energy of 1–10 eV.
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| * The elementary step in physisorption from a gas phase does not involve an activation energy. Chemisorption often involves an activation energy.
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| * For physisorption, under appropriate conditions, gas phase molecules can form multilayer adsorption. In chemisorption, molecules are adsorbed on the surface by valence bonds and only form monolayer adsorption.
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| ==See also==
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| *[[Adsorption]]
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| *[[Chemisorption]]
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| *[[van der Waals force]]
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| ==References==
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| {{reflist}}
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| [[Category:Surface chemistry]]
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