an introduction to surface chemistry-doc

8/12/2019 An Introduction to Surface Chemistry-Doc

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An Introduction to Surface

Chemistry written byDr. Roger Nix

Department of Chemistry

1. Structure of Metallic Surfaces

1.1 Surface Structure of Metals

In most technological applications, metals are used either in a finely divided form (e.g.supported metal catalysts or in a massive, polycrystalline form (e.g. electrodes,mechanical fabrications.

!t the microscopic level, most materials, with the notable exception of a few trulyamorphous specimens, can be considered as a collection or aggregate of single crystalcrystallites. "he surface chemistry of the material as a whole is therefore cruciallydependent upon the nature and type of surfaces exposed on these crystallites.In principle,therefore, we can understand the surface properties of any material if we

#. $now the amount of each type of surface exposed , and%. have detailed $nowledge of the properties of each and every type of surface plane.

("his approach assumes that we can neglect the possible influence of crystal defects andsolid state interfaces on the surface chemistry

It is therefore vitally important that we can independently study different, well&definedsurfaces. "he most commonly employed techni'ue, is to prepare macroscopic (i.e. sie )cm single crystals of metals and then to deliberately cut&them in a way which exposes alarge area of the specific surface of interest.

*ost metals only exist in one bul$ structural form & the most common metallic crystalstructures being +
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bcc body-centred cubicfcc face-centred cubichcp hexagonal close packed

or each of these crystal systems, there are in principle an infinite number of possible

surfaces which can be exposed. In practice, however, only a limited number of planes(predominantly the so&called -low&indexsurfaces are found to exist in any significantamount and we can concentrate our attention on these surfaces. urthermore, it is possibleto predict the ideal atomic arrangement at a given surface of a particular metal byconsidering how the bul$ structure is intersected by the surface. irstly, however, we needto loo$ in detail at the bul$ crystal structures.

I. The hcpandfccstructures

"he hcpandfccstructures are closely related + they are both based upon stac$ing layers ofatoms, where the atoms are arranged in a close&pac$ed hexagonal manner within the

individual layer.

"he atoms of the next layer of the structure will preferentially sit in some of the hollows inthe first layer & this gives the closest approach of atoms in the two layers and therebymaximies the cohesive interaction.


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hen it comes to deciding where the next layer of atoms should be positioned there aretwo choices & these differ only in the relative positions of atoms in the #st and /rd layers.

In the structure on the left the atoms of the /rd layer sit directly above those in the #st layer& this gives rise to the characteristic ..!0!0!.. pac$ing se'uence of the hcpstructure.

In the structure on the right the atoms of the /rd layer are laterally offset from those in boththe #st and %nd layers, and it is not until the 1th layer that the se'uence begins to repeat."his is the ..!0C!0C.. pac$ing se'uence of thefccstructure. 0ecause of their commonorigin, both of these structures share common features +

#. "he atoms are close pac$ed%. 2ach atom has #% nearest neighbours ( i.e. CN 3 #%

a! fccstructure

!lthough it is not immediately obvious, the ..!0C!0C.. pac$ing se'uence of the fccstructure gives rise to a three&dimensional structure with cubic symmetry ( hence thename 4 .

fccstructure

It is the cubic unit cell that is commonly used to illustrate this structure & but the fact thatthe origin of the structure lies in the pac$ing of layers of hexagonal symmetry should notbe forgotten.


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"he above diagram shows the atoms of one of the hexagonal close&pac$ed layershighlighted in shades of red, and the atoms of another highlighted in shades of green.

b! hcpstructure

"he ..!0!0!.. pac$ing se'uence of the hcpstructure gives rise to a three&dimensional unitcell structure whose symmetry is more immediately related to that of the hexagonally&closepac$ed layers from which it is built, as illustrated in the diagram below.

II. The bccstructure

"he bccstructure has very little in common with thefccstructure & except the cubic natureof the unit cell. *ost importantly, it differs from the hcpandfccstructures in that it is not a

close&pac$ed structure.


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bcc structure

hat is the co&ordination number of atoms in this structure 5

"here do #e go from here $

!n ordered surface may be obtained by cutting the three&dimensional bul$ structure of asolid along a particular plane to expose the underlying array of atoms. "he way in whichthis plane intersects the three&dimensional structure is very important and is defined byusingMiller Indices& this notation is commonly used by both surface scientists andcrystallographers since an idealsurface of a particular orientation is nothing more than alattice plane running through the /D crystal with all the atoms removed from one side ofthe plane.

In order to see what surface atomic structures are formed on the various *iller indexsurfaces for each of the different crystal systems we need to consider how the lattice planesbisect the three&dimensional atomic structure of the solid. "o pursue this 'uestion for thefcc, hcpand bccsystems you should select the appropriate option from the menu afterexiting from this section. !s you might expect, however, the various surfaces exhibit awide range of+

#. 6urface symmetry%. 6urface atom coordination

and most importantly this results in substantial differences in 77.

/. 8hysical properties ( electronic characteristics etc. , and1. 6urface chemical reactivity (catalytic activity, oxidation resistance etc.

1.% Surface Structure of fcc Metals

*any of the technologically most important metals possess thefccstructure + for examplethe catalytically important precious metals ( 8t, Rh, 8d all exhibit anfccstructure.
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"he low index faces of this system are the most commonly studied of surfaces + as we shallsee they exhibit a range of

1. Surface symmetry

%. Surface atom coordination

&. Surface reacti'ity

I. The fcc 1((! surface

"he (#99 surface is that obtained by cutting thefccmetal parallel to the front surface of thefcccubic unit cell & this exposes a surface (the atoms in blue with an atomic arrangementof 1&fold symmetry

fcc unit cell1((! face

"he diagram below shows the conventional birds&eye view of the (#99 surface & this isobtained by rotating the preceding diagram through 1:; to give a view which emphasisesthe 1&fold (rotational symmetry of the surface layer atoms.

"he tops of the second layer atoms are


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"here are several other points worthy of note +

#. !ll the surface atoms are e'uivalent%. "he surface is relatively smooth at the atomic scale/. "he surface offers various adsorption sites for molecules which have different local

symmetries and lead to different coordination geometries & specifically there are +

o =n&top sites (above a single metal atomo 0ridging sites, between two atomso >ollow sites, between four atoms

Depending upon the site occupied, an adsorbate species (with a single point of attachmentsto the surface is therefore li$ely to be bonded to either one, two or four metal atoms.

II. The fcc11(! surface

"he (##9 surface is obtained by cutting thefccunit cell in a manner that intersects thexandyaxes but not thez&axis & this exposes a surface with an atomic arrangement of %&foldsymmetry.

fcc unit cell

11(! face

"he diagram below shows the conventional birds&eye view of the (##9 surface &emphasising the rectangular symmetry of the surface layer atoms. "he diagram has beenrotated such that the rows of atoms in the first atomic layer now run vertically, rather thanhoriontally as in the previous diagram.


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It is clear from this view that the atoms of the topmost layer are much less closely pac$edthan on the (#99 surface & in one direction (along the rows the atoms are in contact i.e. thedistance between atoms is e'ual to twice the metallic(atomic radius, but in the orthogonaldirection there is a substantial gap between the rows.

"his means that the atoms in the underlying second layer are also, to some extent, exposedat the surface

11(! surface plane

e.g. Cu11(!

"he preceding diagram illustrates some of those second layer atoms, exposed at the bottomof the troughs.

In this case, the determination of atomic coordination numbers re'uires a little more carefulthought + one way to double&chec$ your answer is to remember that the CN of atoms in thebul$ of thefccstructure is #%, and then to subtract those which have been removed fromabove in forming the surface plane.

hat is the coordination number of the topmost layer atoms 5

If we compare this coordination number with that obtained for the (#99 surface, it is worthnoting that the surface atoms on a more open (-rougher- surface have a lower CN & thishas important implications when it comes to the chemical reactivityof surfaces.
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Do the atoms in the second layer have the bul$ coordination 5

)o& the fact that they are clearly exposed (visible at the surface implies that they have alower CN than they would in the bul$.

hat is the coordination number of these second layer atoms 5

In summary, we can note that

#. !ll first layer surface atoms are e'uivalent, but second layer atoms are also exposed%. "he surface is atomically rough, and highly anisotropic/. "he surface offers a wide variety of possible adsorption sites, including +

o =n&top siteso 6hort bridging sites between two atoms in a single rowo ?ong bridging sites between two atoms in adigher coordination sites ( in the troughs

III. The fcc 111! surface

"he (### surface is obtained by cutting thefccmetal in such a way that the surface planeintersects thex&,y& andz& axes at the same value & this exposes a surface with an atomicarrangement of /&fold ( apparently @&fold, hexagonal symmetry. "his layer of surfaceatoms actually corresponds to one of the close&pac$ed layers on which the fccstructure isbased.

fcc unit cell

111! face

"he diagram below shows the conventional birds&eye view of the (### surface &emphasising the hexagonal pac$ing of the surface layer atoms. 6ince this is the mostefficient way of pac$ing atoms within a single layer, they are said to be -close&pac$ed-.
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111! surface planee.g. *t111!

hat is the coordination number of the surface layer atoms 5

"he following features are worth noting A

#. !ll surface atoms are e'uivalent and have a relatively high CN%. "he surface is almost smooth at the atomic scale/. "he surface offers the following adsorption sites +

o =n&top siteso 0ridging sites, between two atomso >ollow sites, between three atoms

I+. ,o# do these surfaces intersect in irregular-shaped samples.

lat surfaces of single crystal samples correspond to a single *iller Index plane and, as we

have seen, each individual surface has a well&defined atomic structure. It is these flatsurfaces that are used in most surface science investigations, but it is worth a brief aside toconsider what type of surfaces exist for an irregular shaped sample (but one that is stillbased on a single crystal. 6uch samples can exhibit facets corresponding to a range ofdifferent *iller Index planes. "his is best illustrated by loo$ing at the (clic$able diagramsbelow.

(i an angled corner (ii a spherical tip

rom the 0!?6!Cpicture gallery of 8rof. B. >ermann, rit&>aber&Institut, 0erlin

SMMA/

Depending upon how anfccsingle crystal is cleaved or cut, flat surfaces of macroscopicdimensions which exhibit a wide range of structural characteristics may be produced.
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"he single crystal surfaces discussed here ( (#99, (##9 (### represent only the mostfre'uently studied surface planes of thefccsystem & however, they are also the mostcommonly occurring surfaces on such metals and the $nowledge gained from studies onthis limited selection of surfaces goes a long way in propagating the development of ourunderstanding of the surface chemistry of these metals.

or further information on other fcc metal surfaces you should ta$e a loo$ at +

6ection #. + =ther 6ingle Crystal 6urfacesIncludes a brief description of high indexfccsurfaceswith illustrative examples.

!tlas of fcc Crystal 6urfaces! -clic$able map- of a wide range offccsurfaces(one part of a useful tutorial on metal crystallographyfrom 8er 6tole, !alborg Eniversity..

1.& Surface Structure of hcp Metals

"his important class of metallic structures includes metals such as Co, Fn, "i Ru.

"he *iller Index notation used to describe the orientation of surface planes for allcrystallographic systems is slightly more complex in this case since the crystal structuredoes not lend itself to description using a standard cartesian set of axes& instead thenotation is based upon three axes at #%9 degrees in the close&pac$ed plane, and one axis(the c&axis perpendicular to these planes. "his leads to a four&digit index structure Ahowever, since the third of these is redundant it is sometimes left out 4

I. The hcp (((1! surface

"his is the most straightforward of the hcpsurfaces since it corresponds to a surface planewhich intersects only the c&axis, being coplanar with the other / axes i.e. it corresponds tothe close pac$ed planes of hexagonally arranged atoms that form the basis of the structure.It is also sometimes referred to as the (99# surface.

(((1! surface planee.g. u(((1!
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"his conventional plan view of the (999# surface shows the hexagonal pac$ing of thesurface layer atoms.

hich fcc surface does it resemble 5

e can summarise the characteristics of this surface by noting that +

#. !ll the surface atoms are e'uivalent and have CN3G%. "he surface is almost smooth at the atomic scale/. "he surface offers the following adsorption sites +

o =n&top siteso 0ridging sites, between two atomso >ollow sites, between three atoms

1.0 Surface Structure of bcc Metals! number of important metals ( e.g. e, , *o have the bcc structure. !s a result of thelow pac$ing density of the bul$ structure, the surfaces also tend to be of a rather opennature with surface atoms often exhibiting rather low coordination numbers.

I. The bcc 1((! surface

"he (#99 surface is obtained by cutting the metal parallel to the front surface of the bcccubic unit cell & this exposes a relatively open surface with an atomic arrangement of 1&foldsymmetry.

bcc unit cell1((! face

"he diagram below shows a plan view of this (#99 surface & the atoms of the second layer(shown on left are clearly visible, although probably inaccessible to any gas phasemolecules.
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bcc1((! surface planee.g. e1((!


Is the coordination of the second layer atoms the same as that of bul$ atoms 5

II. The bcc 11(! surface

"he (##9 surface is obtained by cutting the metal in a manner that intersects the x and yaxes but creates a surface parallel to the &axis & this exposes a surface which has a higheratom density than the (#99 surface.

bcc unit cell11(! face

"he following diagram shows a plan view of the (##9 surface & the atoms in the surfacelayer strictly form an array of rectangular symmetry, but the surface layer coordination ofan individual atom is 'uite close to hexagonal.
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bcc11(! surface planee.g. e11(!


III. The bcc 111! surface

"he (### surface of bcc metals is similar to the (### face of fcc metals only in that itexhibits a surface atomic arrangement exhibiting /&fold symmetry & in other respects it isvery different.

Top +ie# 2

bcc111! surface plane

e.g. e111!

In particular it is a very much more open surface with atoms in both the second and thirdlayers clearly visible when the surface is viewed from above. "his open structure is alsoclearly evident when the surface is viewed in cross&section as shown in the diagram belowin which atoms of the various layers have been annotated.

Side +ie# 2

bcc111! surface plane

e.g. e111!

1.3 4nergetics of Solid Surfaces
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!ll surfaces are energetically unfavourable in that they have a positive free energy offormation. ! simple rationalisation for why this must be the case comes from consideringthe formation of new surfaces by cleavage of a solid and recogniing that bonds have to bebro$en between atoms on either side of the cleavage plane in order to split the solid andcreate the surfaces. 0rea$ing bonds re'uires wor$ to be done on the system, so the surface

free energy (surface tension contribution to the total free energy of a system musttherefore be positive.

"he unfavourable contribution to the total free energy may, however, be minimised inseveral ways +

#. 5y reducing the amount of surface area exposed%. 5y predominantly exposing surface planes #hich ha'e a lo# surface free

energy/. 5y altering the local surface atomic geometry in a #ay #hich reduces the

surface free energy

"he first and last points are considered elsewhere ( #.H 8articulate *etals, #.@ Relaxationand Reconstruction, respectively & only the second point will be considered further here.

=f course, systems already possessing a high surface energy (as a result of the preparationmethod will not always readily interconvert to a lower energy state at low temperaturesdue to the $inetic barriers associated with the restructuring & such systems (e.g. highlydispersed materials such as those in colloidal suspensions or supported metal catalysts arethus -metastable-.

It should also be noted that there is a direct correspondence between the concepts of

-surface stability- and -surface free energy- i.e. surfaces of low surface free energy will bemore stable and vice versa.

=ne rule of thumb, is that the most stable solid surfaces are those with +

#. a high surface atom density%. surface atoms of high coordination number

(Note & the two factors are obviously not independent, but are inevitably stronglycorrelated.

Conse'uently, for example, if we consider the individual surface planes of an fcc metal,then we would expect the stability to decrease in the order

fcc 111! 6 fcc 1((! 6 fcc 11(!

"arning& the above comments strictly only apply when the surfaces are in vacuum. "hepresence of a fluid above the surface ( gas or li'uid can drastically affect the surface freeenergies as a result of the possibility of molecular adsorption onto the surface. 8referential
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adsorption onto one or more of the surface planes can significantly alter the relativestabilities of different planes & the influence of such effects under reactive conditions (e.g.the high pressurehigh temperature conditions pertaining in heterogeneous catalysis ispoorly understood.

1.7 elaxation 8 econstruction of Surfaces

"he phenomena of relaxation and reconstruction involve rearrangements of surface ( andnear surface atoms, this process being driven by the energetics of the system i.e. thedesire to reduce the surface free energy ( see#.: 2nergetics of 6urfaces. !s with allprocesses, there may be $inetic limitations which prevent or hinder these rearrangements atlow temperatures.

0oth processes may occur with clean surfaces in ultrahigh vacuum, but it must beremembered that adsorption of species onto the surface may enhance, alter or even reversethe process 4

I. elaxation

Relaxation is a small and subtle rearrangement of the surface layers which maynevertheless be significant energetically, and seems to be commonplace for metal surfaces.It involves ad


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elaxed Surfaced1-%9 dbulk!

"he lower picture shows the relaxed surface + the first layer of atoms is typically drawn inslightly towards the second layer (i.e. d#&%J dbul$

e can consider what might be the driving force for this process at the atomic level ....

If we use a localised model for the bonding in the solid then it is clear that an atom in thebul$ is acted upon by a balanced, symmetrical set of forces.

=n the other hand, an atom at the unrelaxed surface suffers from an imbalance of forcesand the surface layer of atoms may therefore be pulled in towards the second layer.


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(hether this is a reasonable model for bonding in a metal is open to 'uestion 4

"he magnitude of the contraction in the first layer spacing is generally small ( J #9 K &

compensating ad


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6ince reconstruction involves a change in the periodicity of the surface and in some casesalso a change in surface symmetry, it is readily detected using surface diffractiontechni'ues (e.g. ?22D R>22D .

"he overall driving force for reconstruction is once again the minimiation of the surfacefree energy & at the atomic level, however, it is not always clear why the reconstructionshould reduce the surface free energy. or some metallic surfaces, it may be that the change

in periodicity of the surface induces a splitting in surface&localied bands of energy levelsand that this can lead to a lowering of the total electronic energy when the band is initiallyonly partly full.

In the case of many semiconductors, the simple reconstructions can often be explained interms of a -surface healing- process in which the co&ordinative unsaturation of the surfaceatoms is reduced by bond formation between ad


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"he minimisation of surface energy means that even single crystal surfaces will not exhibitthe ideal geometry of atoms to be expected by truncating the bul$ structure of the solidparallel to a particular plane. "he differences between the real structure of the clean surfaceand the ideal structure may be imperceptibly small (e.g. a very slight surface relaxation ormuch more mar$ed and involving a change in the surface periodicity in one or more of the

main symmetry directions (surface reconstruction .

1.: *articulate Metals

!s mentioned in the Introduction, macroscopic single crystals of metals are not generallyemployed in technological applications.

*assive metallic structures (electrodes etc. are polycrystalline in nature & the sie ofindividual crystallites being determined by the mechanical treatment and thermal history ofthe metal concerned. Nevertheless, the nature and properties of the exposed polycrystalline,metal surface is still principally determined by the characteristics of the individual crystal

surfaces present. urthermore, the proportions in which the different crystal surfaces occuris controlled by their relative thermodynamic stabilities. "hus, a macroscopic piece of anfcc metal will generally expose predominantly (###&type surface planes.

! more interesting case for consideration is that of metals in a highly dispersed system &the classic example of which is a supported metal catalyst (such as those employed in thepetrochemical industries and automotive catalytic converters. In such catalysts the averagemetal particle sie is invariably sub&micron and may be as small as # nm . "hese metalparticles are often tiny single crystals or simple twinned crystals.

"he shape of these small crystals is principally determined by the surface free energy

contribution to the total energy. "here are two ways in which the surface energy can bereduced for a crystal of fixed mass volume +

#. 0y minimiing the surface area of the crystallite%. 0y ensuring that only surfaces of low surface free energy are exposed.

If matter is regarded as continuous then the optimum shape for minimiing the surface freeenergy is a sphere (since this has the lowest surface areavolume ratio of any /D ob


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=ctahedron exposing symmetry&related

fcc(###&type faces

( Note + there are different, but crystallographically&e'uivalent, surface planes which havethe (### surface structure & the O###P faces. "hey are related by the symmetry elements of

the cubic fcc system.

! compromise between exposing only the lowest energy surface planes and minimiing thesurface area is obtained by truncating the vertices of the octahedron & this generates a cubo&

octahedral particle as shown below, with (###&type surfaces and @ smaller, (#99&typesurfaces and gives a lower (surface area volume ratio.

Crystals of this general form are often used as conceptual models for the metal particles insupported catalysts.

"he atoms in the middle of the O###P faces show the expected CN3G characteristic of the(### surface. 6imilarly, those atoms in the centre of the O#99P surfaces have thecharacteristic CN3 of the (#99 surface.

>owever, there are also many atoms at the corners and intersection of surface planes on theparticle which show lower coordination numbers.

hat is the lowest coordination number exhibited by a surface atom on thiscrystallite 5
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"his model for the structure of catalytic metal crystallites is not always appropriate + it isonly reasonable to use it when there is a relatively wea$ interaction between the metal andthe support phase (e.g. many silica supported catalysts.

! stronger metal&support interaction is li$ely to lead to increased -wetting- of the support

by the metal, giving rise to +

a greater metal&support contact area a significantly different metal particle morphology

or example

In the case of a strong metal&support interaction the metaloxide interfacial free energy islow and it is inappropriate to consider the surface free energy of the metal crystallite inisolation from that of the support.

=ur $nowledge of the structure of very small particles comes largely from high resolutionelectron microscopy (>R2* studies & with the best modern microscopes it is possible todirectly observe such particles and resolve atomic structure.

2xamples Dr. D. Qefferson, Eniversity of Cambridge (EB>R2* acility, North estern Eniversity (E6

1.;


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"hese will not be covered in any depth, but a few illustrative examples are given below togive you a flavour of the additional complexity involved when considering such surfaces.

,igh Index Surfaces of Metals

>igh index surfaces are those for which one or more of the *iller Indices are relativelylarge numbers. "he most commonly studied surfaces of this type are vicinal surfaceswhichare cut at a relatively small angle to one of the low index surfaces. "he ideal surfaces canthen be considered to consist of terraces which have an atomic arrangement identical withthe corresponding low index surface, separated by monatomic steps (steps which are asingle atom high.

8erspective view of thefcc(HH: surface

!s seen above, the ideal fcc(HH: surface has a regular array of such steps and these stepsare both straight and parallel to one another.

hat is the coordination number of a step atom on this surface 5

0y contrast a surface for which all the *iller indices differ must not only exhibit steps butmust also contain $in$s in the steps. !n example of such a surface is the fcc(#9..H surface& the ideal geometry of which is shown below.

8erspective view of the fcc(#9..Hsurface
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hat is the lowest coordination number exhibited by any of the atoms on this surface5

Real vicinal surfaces do not, of course, exhibit the completely regular array of steps and$in$s illustrated for the ideal surface structures, but they do exhibit this type of step and

terrace morphology. "he special adsorption sites available ad


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or further information on the surface structure of compound materials you should ta$e aloo$ at +

=xide 6urfaces The Surface Science of Metal Oxides, by S.2. >enri8.!. Cox (CE8, #GG1

6urfaces of compounds with the sodium chloride(NaCl, caesium chloride (CsCl and cubicincblende (Fn6 structure.

"he 6urface 2xplorer(based at the rit >aber Institon&line interactive surface structure utility.

6urfaces of compound semiconductors, alloys andoxides.

allery of 8icturesfrom the NI6" 6urface 6tructure (courtesy of 8rof. B. >ermann.

%. Adsorption of Molecules on Surfaces

%.1 Introduction to Molecular Adsorption"he adsorption of molecules on to a surface is a necessary prere'uisite to any surfacemediated chemical process.

or example, in the case of a surface catalysed reaction it is possible to brea$ down thewhole continuously&cycling process into the following five basic steps +

#. Diffusion of reactants to the active surface%. !dsorption of one or more reactants onto the surface/. 6urface reaction

1. Desorption of products from the surface:. Diffusion of products away from the surface

"he above scheme not only emphasises the importance of the adsorption process but alsoits reverse & namely desorption. It is these two processes which are considered in this6ection.

)otes on Terminology 2

Substrate& fre'uently used to describe the solid surface onto which adsorption can occurAthe substrate is also occasionally (although not here referred to as the adsorbent.

Adsorbate& the general term for the atomic or molecular species which are adsorbed (or arecapable of being adsorbed onto the substrate.

Adsorption& the process in which a molecule becomes adsorbed onto a surface of anotherphase (note & to be distinguished from absorption which is used when describing upta$einto the bul$ of a solid or li'uid phase
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Coverage& a measure of the extent of adsorption of a species onto a surface (unfortunatelythis is defined in more than one way 4 . Esually denoted by the lower case ree$ -theta-,

Exposure& a measure of the amount of gas which a surface has seenA more specifically, it isthe product of the pressure and time of exposure (normal unit is the ?angmuir, where # ? 3

#9&@

"orr s .

%.% ,o# do Molecules 5ond to Surfaces $

"here are two principal modes of adsorption of molecules on surfaces +

*hysical Adsorption *hysisorption !Chemical Adsorption Chemisorption !

"he basis of distinction is the nature of the bonding between the molecule and the surface.ith ...

hysical Adsorption+ the only bonding is by wea$ San der aals & type forces. "here is nosignificant redistribution of electron density in either the molecule or at the substratesurface.

Che!isorption+ a chemical bond, involving substantial rearrangement of electron density,is formed between the adsorbate and substrate. "he nature of this bond may lie anywherebetween the extremes of virtually complete ionic or complete covalent character.

Typical Characteristics of Adsorption *rocesses

Chemisorption *hysisorption

"emperature Range(over which adsorptionoccurs

Sirtually unlimited(but a given molecule mayeffectively adsorb only over asmall range

Near or below thecondensation point of the gas(e.g. Te J #99 B, C=%J %99B

!dsorption 2nthalpyide range (related to thechemical bond strength &typically 19 & 99 $Q mol

Related to factors li$emolecular mass and polaritybut typically :&19 $Q mol(i.e.) heat of li'uefaction

Crystallographic 6pecificity(variation between differentsurface planes of the samecrystal

*ar$ed variation betweencrystal planes

Sirtually independent ofsurface atomic geometry

Nature of !dsorption=ften dissociative*ay be irreversible

Non&dissociativeReversible

6aturation Epta$e ?imited to one monolayer *ultilayer upta$e possible


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Binetics of !dsorptionSery variable & often anactivated process

ast & since it is a non&activated process

"he most definitive method for establishing the formation of a chemical bond between theadsorbing molecule and the substrate ( i.e. chemisorption is to use an appropriate

spectroscopic techni'ue, for example

IR ( see 6ection :.1 & to observe the vibrational fre'uency of the substrateadsorbate bond

E86 ( see 6ection :./ & to monitor intensity energy shifts in the valence orbitals of theadsorbate and substrate

%.& Adsorption =inetics& "he Rate of !dsorption

"he rate of adsorption,"ads, of a molecule onto a surface can be expressed in the same

manner as any $inetic process. or example, when it is expressed in terms of the partialpressure of the molecule in the gas phase above the surface+

Rads> k' Px where+ x& $inetic order

#$& rate constant

& partial pressure

If the rate constant is then expressed in an !rrhenius form, then we obtain a $inetice'uation of the form +

Rads>A exp -Ea?RT!.Px

whereEais the activation energy for adsorption, andAthepre-exponential %fre&uency'factor.

It is much more informative, however, to consider the factors controlling this process at themolecular level....

"he rate of adsorption is governed by

#. the rate of arrival of molecules at the surface%. the proportion of incident molecules which undergo adsorption

i.e. we can express the rate of adsorption (per unit area of surface as a product of theincident molecular flux,(, and the stic$ing probability , S.

Rads>S . F Lmolecules m&%s M


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"he flux of incident molecules is given by the >ert&Bnudsen e'uation

lux , F>P? %mkT!1?% L molecules m&%sMwhere

& gas pressure L N m&%M

!& mass of one molecule L $g MT& temperature L B M

"he stic$ing probability is clearly a property of the adsorbate substrate system underconsideration but must lie in the range 9 J SJ #A it may depend upon various factors &foremost amongst these being the existing coverage of adsorbed species ( and thepresence of any activation barrier to adsorption. In general ,therefore ,

S>f! . exp -Ea?RT!

where, once again,Eais the activation energy for adsorption and f( is some, as yetundetermined, function of the existing surface coverage of adsorbed species.

Combining the e'uations for Sand(yields the following expression for the rate ofadsorption +

Notes +

#. "he above e'uation indicates that the rate of adsorption is expected to be first orderwith regard to the partial pressure of the molecule in the gas phase above thesurface.

%. It should be recognised that the activation energy for adsorption may itself bedependent upon the surface coverage , i.e.Ea3E(.

/. If it is further assumed that the stic$ing probability is directly proportional to theconcentration of vacant surface sites (which would be a reasonable firstapproximation for non&dissociative adsorption then f( is proportional to (#& Awhere, in this instance, is the fraction of sites which are occupied (i.e. the

?angmuir definition of surface coverage.or a discussion of some of the factors which determine the magnitude of the activationenergy of adsorption you should see 6ection%.1which loo$s at the typical 82 curveassociated with various types of adsorption process.

4stimating Surface Co'erages arising as a result of @as 4xposure
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If a surface is initially clean and it is then exposed to a gas pressure under conditions wherethe rate of desorption is very slow, then the coverage of adsorbed molecules may initiallybe estimated simply by consideration of the $inetics of adsorption.

!s noted above, the rate of adsorption is given by + Rads>S . F

i.e.

where + )adsis the number of adsorbed species per unit area of surface.

In general, this e'uation must be integrated to obtain an expression for )ads, since thestic$ing probability is coverage (and hence also time dependent.

>owever, if it is assumed that the stic$ing probability is essentially constant (which may bea reasonable approximation for relatively low coverages, then this integration simplyyields+

%.0 *4 Cur'es 8 4nergetics of Adsorption

In this section we will consider both the energetics of adsorption and factors whichinfluence the $inetics of adsorption by loo$ing at the -potential energy diagramcurve- for

the adsorption process.

"he potential energy curve for the adsorption process is a representation of the variation ofthe energy (82 orE of the system as a function of the distance (d of an adsorbate from asurface.

ithin this simple one&dimensional (#D model, the only variable is the distance (d of theadsorbing molecule from the substrate surface. "hus, the energy of the system is a functiononly of this variable i.e.E3E(d


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It should be remembered that this is a very simplistic model which neglects many otherparameters which influence the energy of the system (a single molecule approaching aclean surface, including for example

the angular orientation of the !olecule

changes in the internal bond angles and bond lengths of the !olecule the position of the !olecule parallel to the surface plane

"he interaction of a molecule with a given surface will also clearly be dependent upon thepresence of any existing adsorbed species, whether these be surface impurities or simplypre&adsorbed molecules of the same type (in the latter case we are starting to consider theeffect of surface coverage on the adsorption characteristics.

Nevertheless it is useful to first consider the interaction of an isolated molecule with aclean surface using the simple #D model. or the purposes of this tutorial we will also notbe overly concerned whether the -energy- being referred to should strictly be the internal

energy, the enthalpy or free energy of the system.

CAS4 I - *hysisorption

In the case of pure physisorption ( e.g. !r metals , the only attraction between theadsorbing species and the surface arises from wea$, van der aals forces.

!s illustrated below, these forces give rise to a shallow minimum in the 82 curve at arelatively large distance from the surface (typically dU 9./ nm before the strong repulsiveforces arising from electron density overlap cause a rapid increase in the total energy.


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"here is no barrier to prevent the atom or molecule which is approaching the surface fromentering this physisorption well, i.e. the process is not activated and the $inetics ofphysisorption are invariably fast.

CAS4 II - *hysisorption Molecular Chemisorption

"he wea$ physical adsorption forces and associated long&range attraction will be present tovarying degrees in all adsorbate substrate systems. >owever, in cases where chemicalbond formation between the adsorbate and substrate can also occur, the 82 curve isdominated by a much deeper chemisorption minimum at shorter values of d.

"he graph above shows the 82 curves due to physisorption and chemisorption separately &in practice, the 82 curve for any real molecule capable of undergoing chemisorption is best

described by a combination of the two curves, with a curve crossing at the point at whichchemisorption forces begin to dominate over those arising from physisorption alone.


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"he minimum energy pathway obtained by combining the two 82 curves is nowhighlighted in red. !ny perturbation of the combined 82 curve from the original, separatecurves is most li$ely to be evident close to the highlighted crossing point.

or clarity, we will now consider only the overall 82 curve +

"he depth of the chemisorption well is a measure of the strength of binding to the surface &in fact it is a direct representation of the energy of adsorption, whilst the location of theglobal minimum on the horiontal axis corresponds to the e'uilibrium bond distance (re for the adsorbed molecule on this surface.

"he energy of adsorption is negative, and since it corresponds to the energy changeupon

adsorption it is better represented as E(adsor Eads. >owever, you will also often findthe depth of this well associated with the enthalpy of adsorption, *(ads.

(Note & the -heat of adsorption- , +, is ta$en to be a positive 'uantity e'ual in magnitudeto the enthalpy of adsorption A i.e. +3 &*(ads


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In this particular case, there is clearly no barrier to be overcome in the adsorption processand there is no activation energy of adsorption (i.e.Eaads3 9 , but do remember thepreviously mentioned limitations of this simple #D model.

"here is of course a significant barrier to the reverse, desorption process & the red arrow in

the diagram below represents the activation energy for desorption.

Clearly in this particular case, the magnitudes of the energy of adsorption and theactivation energy for desorption can also be e'uated i.e.

Eades3 E(ads or Eades) &*(ads

CAS4 III - *hysisorption Bissociati'e Chemisorption

In this case the main differences arise from the substantial changes in the 82 curve for the

chemisorption process

!gain, we start off with the basic 82 curve for the physisorption process which representshow the molecule can wea$ly interact with the surface +


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If we now consider a specific molecule such as >%and initially treat it as being completelyisolatedfrom the surface ( i.e. when the distance, d, is very large then a substantialamount of energy has to be put into the system in order to cause dissociation of themolecule.

>% > V >

& this is the bond dissociation energy L,(>&> M, some 1/: $Q molor 1.: eS.

"he red dot in the diagram above thus represents two hydrogen atoms, e'uidistant (and along distance from the surface and also now well separated from each other. If these atomsare then allowed to approach the surface they may ultimately both form strong chemicalbonds to the substrate .... this corresponds to the minimum in the red curve whichrepresents the chemisorption 82 curve for the two > atoms.

In reality, of course, such a mechanism for dissociative hydrogen chemisorption is notpractical & the energy downpayment associated with brea$ing the >&> bond is far toosevere.

Instead, a hydrogen molecule will initially approach the surface along the physisorptioncurve. If it has sufficient energy it may pass straight into the chemisorption well ( -directchemisorption- ....


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or, alternatively, it may first undergo transient physisorption & a state from which it canthen either desorb bac$ as a molecule into the gas phase or cross over the barrier into thedissociated, chemisorptive state (as illustratedsche!aticallybelow.

In this latter case, the molecule can be said to have undergone -precursor&mediated-chemisorption.

"he characteristics of this type of dissociative adsorption process are clearly going to bestrongly influenced by the position of the crossing point of the two curves (molecularphysisorption vWs dissociative chemisorption & relatively small shifts in the position ofeither of the two curves can significantly alter the sie of any barrier to chemisorption.

In the example immediately below there is no direct activation barrier to dissociative

adsorption & the curve crossing is below the initial -ero energy- of the system.


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whilst, in this next case 7.

there is a substantial barrier to chemisorption. 6uch a barrier has a ma


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Clearly, from the diagram

Eades&Eaads3 & Eads

but, since the activation energy for adsorption is nearly always very much smaller than thatfor desorption, and the difference between the energy and enthalpy of adsorption is alsovery small, it is still 'uite common to see the relationship

Eades ) &*ads

or a slightly more detailed treatment of the adsorption process, you are referred to thefollowing examples of *ore Complex 82 Curves *ulti&Dimensional 82 6urfaces.

%.3 Adsorbate @eometries 8 Structures on Metalse can address the 'uestion of what happens when a molecule becomes adsorbed onto asurface at two levelsA specifically we can aim to identify

#. the nature of the adsorbed species and its local adsorption geometry (i.e. itschemical structure and co&ordination to ad


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Chemisorption of ,ydrogen and ,alogens

*ydrogen %*1'

In the >%molecule, the valence electrons are all involved in the >&> &bond and there are

no additional electrons which may interact with the substrate atoms. Conse'uently,chemisorption of hydrogen on metals is almost invariably a dissociative process in whichthe >&> bond is bro$en, thereby permitting the hydrogen atoms to independently interactwith the substrate (see 6ection %.1for a description of the energetics of this process. "headsorbed species in this instance therefore are hydrogen atoms.

"he exact nature of the adsorbed hydrogen atom complex is generally difficult to determineexperimentally, and the very small sie of the hydrogen atom does mean that migration ofhydrogen from the interface into sub&surface layers of the substrate can occur with relativeease on some metals (e.g. 8d, rare earth metals.

"he possibility of molecular >%chemisorption at low temperatures cannot be entirelyexcluded, however, as demonstrated by the discovery of molecular hydrogen transitionmetal compounds, such as (%&>% (C=/(8i&8r/ /, in which both atoms of the hydrogenmolecule are coordinated to a single metal centre.

*alogens %(1. Cl1. 2r1etc0'

>alogens also chemisorb in a dissociative fashion to give adsorbed halogen atoms. "hereasons for this are fairly clear & in principle a halogen molecule could act as a ?ewis baseand bind to the surface without brea$age of the T&T bond, in practice the lone pairs arestrongly held by the highly electronegative halogen atom so any such interaction would be

very wea$ and the thermodynamics lie very heavily in favour of dissociative adsorptionL i.e. D(T&T V D(*&T% JJ % D(*&T M. Clearly the $inetic barrier to dissociation mustalso be low or non&existent for the dissociative adsorption to occur readily.

!nother way of loo$ing at the interaction of a halogen molecule with a metal surface is asfollows + the significant difference in electronegativity between a typical metal and halogenis such that substantial electron transfer from the metal to halogen is favoured. If a halogenmolecule is interacting with a metal surface then this transferred electron density will enterthe X antibonding orbital of the molecule, thereby wea$ening the T&T bond. !t the sametime the build&up of negative charge on the halogen atoms enhances the strength of themetal&halogen interaction. "he net result of these two effects when ta$en to their limit is

that the halogen molecule dissociates and the halogen atoms interact with the metal with astrong ionic contribution to the bonding.

>alogen atoms tend to occupy high co&ordination sites on the surface & for example, the /&fold hollow site onfcc(### surfaces (A and the 1&fold hollow site onfcc(#99 surfaces(5.
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(A lan 3ie (5

"his behaviour is typical of atomic adsorbates which almost invariably endeavour tomaximise their co&ordination and hence prefer to occupy the highest&available co&ordination site on the surface.

!s a result of the electron transfer from the metal substrate to the halogen atoms, eachadsorbed atom is associated with a significant surface dipole.

Cross-section

=ne conse'uence of this is that there are repulsive (dipole&dipole interactions between theadsorbed atoms, which are especially evident at higher surface coverages and which canlead to a substantial reduction in the enthalpy of adsorption at specific coverages (if these

coverages mar$ a watershed, above which the atoms are forced to occupy sites which aremuch closer together.

!nother feature of the halogen adsorption chemistry of some metals is the transition froman adsorbed surface layer to surface compound formation at high gas exposures.

Chemisorption of )itrogen and


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#. &donor interaction, in which the charge transfer is from the occupied molecular &bonding molecular orbital of the molecule into vacant orbitals of &symmetry onthe metal (i.e. * =%, and

%. &acceptor interaction, in which an occupied metal d&orbital of the correctsymmetry overlaps with empty X orbitals of the molecule and the charge transfer

is from the surface to the molecule (i.e. * =% .

!lthough the interaction of the molecule with the surface is generally wea$, one mightexpect that there might be a substantial barrier to dissociation due to the high strength (andhigh dissociation enthalpy of the =3= bond. Nevertheless on most metal surfaces,dissociation of oxygen is observed to be facile which is related to the manner in which theinteraction with the surface can mitigate the high intrinsic bond energy (see 6ection %.1and thereby facilitate dissociation.

=nce formed, oxygen atoms are strongly bound to the surface and, as noted previously,will tend to occupy the highest available co&ordination site. "he strength of the interaction

between adsorbate and substrate is such that the ad


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#. =n the reactive surfaces of metals from the left&hand side of the periodic table (e.g.Na, Ca, "i, rare earth metals the adsorption is almost invariably dissociative,leading to the formation of adsorbed carbon and oxygen atoms (and thereafter tothe formation of surface oxide and oxy&carbide compounds.

%. 0y contrast, on surfaces of the metals from the right hand side of the d&bloc$ (e.g.

Cu, !g the interaction is predominantly molecularA the strength of interactionbetween the C= molecule and the metal is also much wea$er, so the *&C= bondmay be readily bro$en and the C= desorbed from the surface by raising the surfacetemperature without inducing any dissociation of the molecule.

/. or the ma


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energy difference between the various adsorption sites available for molecular C=chemisorption appears therefore to be very small.

L ! description of the nature of the bonding in a terminal C=&metal complex, in terms of asimple molecular orbital model, is given in 6ection :.1M

Chemisorption of Ammonia and other @roup +?+I ,ydrides

!mmonia has lone pairs available for bonding on the central nitrogen atom and may bondwithout dissociation to a single metal atom of a surface, acting as a ?ewis base, to give apseudo&tetrahedral co&ordination for the nitrogen atom.

!lternatively, progressive dehydrogenation may occur to give surface N>x(x3 %,#,9species and adsorbed hydrogen atoms, i.e.

N>/ N>%(ads V >(ads N>(ads V % >(ads N(ads V / >(ads

!s the number of hydrogens bonded to the nitrogen atom is reduced, the adsorbed specieswill tend to move into a higher co&ordination site on the surface (thereby tending tomaintain the valence of nitrogen.

,eco!position frag!ents of a!!onia on an fcc%444' surface(8icture adapted from the0!?6!C 8icture alleryby B. >ermann, rit&>aber&Institut, 0erlin

=ther roup S and roup SI hydrides (e.g. 8>/, >%=, >%6 exhibit similar adsorptioncharacteristics to ammonia.

Chemisorption of nsaturated ,ydrocarbons
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Ensaturated hydrocarbons (al$enes, al$ynes, aromatic molecules etc. all tend to interactfairly strongly with metal atom surfaces. !t low temperatures (and on less reactive metalsurfaces the adsorption may be molecular, albeit perhaps with some distortion of bondangles around the carbon atom.

2thene, for example, may bond to give both a &complex (A or a di& adsorption complex(5+

(A Che!isorbed (5Ethene

L urther examples + models of chemisorbed ethene and ethyne on Cu(###M

!s the temperature is raised, or even at low temperatures on more reactive surfaces (inparticular those that bind hydrogen strongly, a stepwise dehydrogenation may occur. =neparticularly stable surface intermediate found in the dehydrogenation of ethene is theethylidynecomplex, whose formation also involves >&atom transfer between the carbonatoms.

Ethylidyne 5

this adsorbate preferentially occupies a

6-fold hollo site to give pseudo-

tetrahedral co-ordination for the carbonato!0

"he ultimate product of complete dehydrogenation, and the loss of molecular hydrogen bydesorption, is usually either carbidic or graphitic surface carbon.

%.7 The Besorption *rocess

!n adsorbed species present on a surface at low temperatures may remain almostindefinitely in that state. !s the temperature of the substrate is increased, however, there

will come a point at which the thermal energy of the adsorbed species is such that one ofseveral things may occur +

#. a molecular species may decompose to yield either gas phase products or othersurface species.

%. an atomic adsorbate may react with the substrate to yield a specific surfacecompound, or diffuse into the bul$ of the underlying solid.

/. the species may desorb from the surface and return into the gas phase.
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"he last of these options is the desorption process. In the absence of decomposition thedesorbing species will generally be the same as that originally adsorbed but this is notnecessarily always the case.

(!n example where it is not is found in the adsorption of some al$ali metals on metallic

substrates exhibiting a high wor$ function where, at low coverages, the desorbing speciesis the al$ali metal ion as opposed to the neutral atom. =ther examples would includecertain isomerisation reactions.

Besorption =inetics

"he rate of desorption,"des , of an adsorbate from a surface can be expressed in the generalform +

Rdes3 k Nx where x& $inetic order of desorption

#& rate constant for the desorption process

)& surface concentration of adsorbed species

"he order of desorption can usually be predicted because we are concerned with anelementary stepof a -reaction- + specifically,

I.Ato!ic or Si!ple Molecular ,esorption

!(ads !(g*(ads *(g

& will usually be a first order process ( i.e.x3 # . 2xamples include 7

Cu(ads (sV Cu(g A desorption of Cu atoms from a surfaceCu C=(ads Cu(sV C=(g A desorption of C= molecules from a Cu surface

II."eco!binative Molecular ,esorption

% !(ads !% (g

& will usually be a second order process ( i.e.x3 % . 2xamples include 7

8t =(ads 8t(sV =% (g A desorption of = atoms as =%from a 8t surfaceNi >(ads Ni(sV >% (g A desorption of > atoms as >%from a Ni surface

"he rate constant for the desorption process may be expressed in an !rrhenius form,

kdes3Aexp -Eades?RT!


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where Eadesis the activation energy for desorption , andAis the pre&exponential factorA this can also be considered to be the -attemptfre'uency-,, at overcoming the barrier to desorption.

"his then gives the following general expression for the rate of desorption

In the particular case of simple molecular adsorption, the pre&exponentialfre'uency factor( may also be e'uated with the fre'uency of vibration of the bond between the moleculeand substrateA this is because every time this bond is stretched during the course of avibrational cycle can be considered an attempt to brea$ the bond and hence an attempt atdesorption.

Surface esidence Times

=ne property of an adsorbed molecule that is intimately related to the desorption $inetics isthesurface residence ti!e& this is the average time that a molecule will spend on thesurface under a given set of conditions (in particular, for a specified surface temperaturebefore it desorbs into the gas phase.

or a first order process such as the desorption step of a molecularly adsorbed species +

M(ads M(gthe average time ( prior to the process occurring is given by +

> 1?k#where ##is the first order rate constant (no proof given.

rom the previously derived desorption formulae we $now that

k#>exp -Eades?RT!and if we also substitute forEa

des

using the approximate relationEades

) &*adsdiscussed in6ection %.1, then we get the following expression for the surface residence time

> oexp -Hads?RT!where + o( 3 # corresponds to the period of vibration of the bond between the adsorbed

molecule and substrate and is fre'uently ta$en to be about #9 /s .


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&. The angmuir Isotherm

&.1 The angmuir Isotherm

henever a gas is in contact with a solid there will be an e'uilibrium established betweenthe molecules in the gas phase and the corresponding adsorbed species (molecules oratoms which are bound to the surface of the solid.

!s with all chemical e'uilibria, the position of e'uilibrium will depend upon a number offactors +

#. "he relative stabilities of the adsorbed and gas phase species involved%. "he temperature of the system (both the gas and surface, although these are

normally the same/. "he pressure of the gas above the surface

In general, factors (% and (/ exert opposite effects on the concentration of adsorbedspecies & that is to say that thesurface coveragemay be increased by raising the gaspressure but will be reduced if the surface temperature is raised.

"he ?angmuir isotherm was developed by Irving ?angmuir in #G#@ to describe thedependence of the surface coverage of an adsorbed gas on the pressure of the gas above thesurface at a fixed temperature. "here are many other types of isotherm ("em$in, reundlich... which differ in one or more of the assumptions made in deriving the expression for thesurface coverageA in particular, on how they treat the surface coverage dependence of theenthalpy of adsorption. hilst the ?angmuir isotherm is one of the simplest, it still

provides a useful insight into the pressure dependence of the extent of surface adsorption.

Important )ote& 6urface Coverage the ?angmuir Isotherm

hen considering adsorption isotherms it is conventional to adopt a definition of surfacecoverage ( which defines the maximum (saturation surface coverage of a particularadsorbate on a given surface always to be unity, i.e. max3 # .This ay of defining the surface coverage differs fro! that usually adopted in surface

sciencewhere the more common practice is to e'uate with the ratio of adsorbate speciesto surface substrate atoms (which leads to saturation coverages which are almost invariablyless than unity.

&.% angmuir Isotherm - deri'ation from eDuilibrium

considerations

e may derive the ?angmuir isotherm by treating the adsorption process as we would anyother e'uilibrium process & except in this case the e'uilibrium is between the gas phasemolecules (*, together with vacant surface sites, and the species adsorbed on the surface.


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"hus, for a non&dissociative (molecular adsorption process we consider the adsorption tobe represented by the following chemical e'uation +

S - E M(g3 S - M

where + S - E, represents a vacant surface site

Note- in riting this e&uation e are !a#ing an inherent assu!ption that there are a fixednu!ber of localised surface sites present on the surface0 This is the first !a7or assu!ption

of the 8ang!uir isother!0

e may now define an e'uilibrium constant (9 in terms of the concentrations of-reactants- and -products-

e may also note that +

L 6 & * M is proportional to the surface coverage of adsorbed molecules, i.e.proportional to

L 6 & X M is proportional to the number of vacant sites, i.e. proportional to (#&) L * M is proportional to the pressure of gas ,

>ence, it is also possible to define another e'uilibrium constant, b, as given below +

Rearrangement then gives the following expression for the surface coverage

which is the usual form of expressing the ?angmuir Isotherm.

!s with all chemical reactions, the e'uilibrium constant, b, is both temperature&dependentand related to the ibbs free energy and hence to the enthalpy change for the process .

Note- b is only a constant %independent of ' if the enthalpy of adsorption is independentof coverage - this is the second !a7or assu!ption of the 8ang!uir Isother!0


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&.& angmuir Isotherm - deri'ation from kinetic

considerations

"he e'uilibrium that may exist between gas adsorbed on a surface and molecules in the gas

phase is a dynamic state, i.e. the e'uilibrium represents a state in which the rate ofadsorption of molecules onto the surface is exactly counterbalanced by the rate ofdesorption of molecules bac$ into the gas phase. It should therefore be possible to derive anisotherm for the adsorption process simply by considering and e'uating the rates for thesetwo processes.

2xpressions for the rate of adsorption and rate of desorption have been derived in 6ections%./ %.@respectively + specifically ,

2'uating these two rates yields an e'uation of the form +

L#M

where the termsf( fW( contain the pre&exponential surface coverage dependence ofthe rates of adsorption and desorption respectively and all other factors have been ta$enover to the right hand side to give a temperature&dependent -constant- characteristic of thisparticular adsorption process, C(T .

e now need to ma$e certain simplifying assumptions ... the first is one of the $eyassumptions of the ?angmuir isotherm

!dsorption ta$es place only at specific localied sites on the surface and the saturation

coverage corresponds to complete occupancy of these sites.

?et us initially further restrict our consideration to a simple case of re'ersible molecularadsorption. i.e.

S - M(g 3 S - M

where S - represents a vacant surface site and S - M the adsorption complex.
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Ender these circumstances it is reasonable to assume coverage dependencies for rates ofthe two processes of the form +

!dsorption, f ! > c1- ! i.e. proportional to the fraction of sites that are unoccupied.Desorption, fF ! > cF i.e. proportional to the fraction of sites which are occupied by

adsorbed molecules.

where is the fraction of sites occupied at e'uilibrium.

Note5 these coverage dependencies are exactly hat ould be predicted by noting that the

forard and reverse processes are ele!entary reaction steps. in hich case it follosfro! standard che!ical #inetic theory that

#. the forard adsorption process ill exhibit #inetics having a first orderdependence on the concentration of vacant surface sites0

%. the reverse desorption process ill exhibit #inetics having a first order dependence

on the concentration of adsorbed !olecules0

6ubstitution into e'uation L#M then yields

where 2(T 3 (cWc.C(T . !fter rearrangement this gives the ?angmuir Isothermexpression for the surface coverage

where b( 3 #2(T is a function of temperature and contains an exponential term of theform

b> ......exp G Eades&Eaads! ?R TH > ...... exp G - Hads?R TH

Conse'uently, bcan only be regarded as a constant with respect to coverage if the enthalpy

of adsorption is itself independent of coverage & this is the second ma


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! given e'uilibrium surface coverage may be attainable at various combinations ofpressure and temperature as highlighted below 7 note that as the temperature is loweredthe pressure re'uired to achieve a particular e'uilibrium surface coverage decreases.

& this is often used as


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It has been shown in previous sections how the value of b is dependent upon the enthalpyof adsorption. It has also


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Step &+ "he Clausius&Clapeyron e'uation

may then be applied to this setof (8&" data and a plot of ( ln8 vWs (#" should give astraight line, the slope ofwhich yields the adsorptionenthalpy.

Note +

the value obtained for the adsorption enthalpy is that pertaining at the surfacecoverage for which the 8&" data was obtained, but steps % / may be repeated fordifferent surface coverages enabling the adsorption enthalpy to be determined overthe whole range of coverages.

this method is applicable only when the adsorption process is thermodynamicallyreversible.

&.3 Applications 2 =inetics of Catalytic eactions

It is possible to predict how the $inetics of certain heterogeneously&catalysed reactions

might vary with the partial pressures of the reactant gases above the catalyst surface byusing the ?angmuir isotherm expression for e'uilibrium surface coverages.

4xample 1 2 nimolecular Becomposition

Consider the surface decomposition of a molecule ! , i.e. the process

A(g A(ads *roducts?et us assume that +

#. "he decomposition reaction occurs uniformly across the surface sites at whichmolecule ! may be adsorbed and is not restricted to a limited number of specialsites.

%. "he products are very wea$ly bound to the surface and, once formed, are rapidlydesorbed.

/. "he rate determining step (rds is the surface decomposition step.


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Ender these circumstances, the molecules of ! adsorbed on the surface are in e'uilibriumwith those in the gas phase and we may predict the surface concentration of ! from the?angmuir isotherm i.e.

> b.P? 1 b.P!

"he rate of the surface decomposition (and hence of the reaction is given by an expressionof the form

ate > k

()ote - e are assu!ing that the deco!position of A%ads' occurs in a si!ple uni!olecularele!entary reaction step and that the #inetics are first order ith respect to the surface

concentration of this adsorbed inter!ediate

6ubstituting for the coverage, , gives us the re'uired expression for the rate in terms of

the pressure of gas above the surface

ate > k b P? 1 b P!

It is useful to consider two extreme limits +

imit 1+ b.P99 1 J then

1 b.P! K 1 and ate K k.b.P

i.e. a first order reaction (with respect to the partial pressure of ! with an apparent

first order rate constant , #$3 #0b."his is the low pressure (or wea$ binding i.e. small b limit + under theseconditions the steady state surface coverage , , of the reactant molecule is verysmall.

imit %+ b.P66 1 J then

1 b.P! K b.P and ate K k

i.e. a ero order reaction (with respect to the partial pressure of ! ."his is the high pressure (or strong binding i.e. large b limit + under these

conditions the steady state surface coverage , , of the reactant molecule is almostunity.

In fact, the rate shows the same pressure variation as does the surface coverage (hardlysurprising since it is directly proportional to


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4xample % 2 5imolecular eaction(between molecular adsorbates

Consider a ?angmuir&>inshelwood reaction of the following type +

A(g3 A(ads

5(g3 5(ads

A(ads 5(ads A5(ads A5(g

e will further assume, as noted in the above scheme, that the surface reaction between thetwo adsorbed species is the rate determining step.

If the two adsorbed molecules are mobile on the surface and freely intermix then the rate ofthe reaction will be given by the following rate expression for the bimolecular surfacecombination step

ate > k ! 0

or a single molecular adsorbate the surface coverage (as given by the ?angmuir isothermis + > b.P? 1 b.P!

here two molecules ( ! 0 are competing for the same adsorption sites then therelevant expressions are (see derivation +
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6ubstituting these into the rate expression gives +

=nce again, it is interesting to loo$ at several extreme limits

imit 1+ b!P!99 1 b0P099 1In this limit ! 0are both very low , and

ate kb!P!b0P0 > k'P!P0i.e.first orderin both reactants

imit %+ b!P!99 1 99b0P0In this limit !9 , 0# , and

ate k b!P!? b0P0 ! > k'P!?P0i.e.first orderin ! , but negative first orderin 0

rom this example it is readily seen that, depending upon the partial pressure and bindingstrength of the reactants, a given model for the reaction scheme can give rise to a variety ofapparent $inetics + this highlights the dangers inherent in the reverse process & namelytrying to use $inetic data to obtain information about the reaction mechanism.

4xample & 2 C< inshelwood mechansim of the following type +

C


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If the two adsorbed molecules are assumed to be mobile on the surface and freely intermixthen the rate of the reaction will be given by the following rate expression for thebimolecular surface combination step

ate > k C= =

here two such species (one of which is molecularly adsorbed, and the other dissociativelyadsorbed are competing for the same adsorption sites then the relevant expressions are(see derivation +

6ubstituting these into the rate expression gives +

=nce again, it is interesting to loo$ at certain limits. If the C= is much more stronglybound to the surface such that bC


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irstly, we need to remind ourselves of the units of pressure +

"he 6I unit of pressure is the 8ascal ( # 8a 3 # N m&% Normal atmospheric pressure ( # atm. is #9#/%: 8a or #9#/ mbar ( # bar 3 #9:

8a .

!n older unit of pressure is the "orr ( # "orr 3 # mm>g . =ne atmosphere is ca.H@9 "orr ( i.e. # "orr 3 #//./ 8a .

hilst the mbar is often used as a unit of pressure for describing the level of vacuum, themost commonly employed unit is still the "orr. ("he 6I unit, the 8a , is almost neverused 4

Classification of the degree of vacuum is hardly an exact science & it very much dependsupon who you are tal$ing to & but as a rough guideline +

Rough (low vacuum + # & #9&/"orr

*edium vacuum + #9&/& #9&:"orr>igh vacuum (>S + #9&@& #9&"orr

Eltrahigh vacuum (E>S + J #9&G"orr

Sirtually all surface studies are carried out under E>S conditions & the 'uestion is #hy5"his is the 'uestion that we will address in 6ection 1.%.

0.% "hy is ,+ reDuired for surface studies $

Eltra high vacuum is re'uired for most surface science experiments for two principalreasons +

#. "o enable atomically clean surfaces to be prepared for study, and such surfaces tobe maintained in a contamination&free state for the duration of the experiment.

%. "o permit the use of low energy electron and ion&based experimental techni'ueswithout undue interference from gas phase scattering.

"o put these points in context we shall now loo$ at the variation of various parameters withpressure

1. @as Bensity

"he gas density is easily estimated from the ideal gas law +

n3 () 3 3 (#0T L molecules m&/M

where + & pressure L N m&%M


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#& 0oltmann constant ( 3 #./ x #9&%/Q BT& temperature L B M

%. Mean ree *ath of *articles in the @as *hase

"he average distance that a particle (atom, electron, molecule .. travels in the gas phasebetween collisions can be determined from a simple hard&sphere collision model (see, forexample, !t$insW 8hysical Chemistry & this 'uantity is $nown as the !ean free pathof theparticle, here denoted by , and for neutral molecules is given by the e'uation +

LmM

where + & pressure L N m&%M#& 0oltmann constant ( 3 #./ x #9&%/Q B T& temperature L B M

& collision cross section L m%M

&. Incident Molecular lux on Surfaces

=ne of the crucial factors in determining how long a surface can be maintained clean (or,alternatively, how long it ta$es to build&up a certain surface concentration of adsorbedspecies is the number of gas molecules impacting on the surface from the gas phase.

"he incidentfluxis the number of incident molecules per unit time per unit area of surface.

(Note & the flux ta$es no account of the angle of incidence, it is merely a summation of allthe arriving molecules over all possible incident angles

or a given set of conditions (.Tetc. the flux is readily calculated using a combination ofthe ideas of statistical physics, the ideal gas e'uation and the *axwell&0oltmann gasvelocity distribution.

Step 4+ it can be readily shown that the incident flux,(, is related to the gas density above

the surface by

L molecules m&%sM

where + n& molecular gas density L molecules m&/Mc& average molecular speed L m sM


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Step 1+ the molecular gas density is given by the ideal gas e'uation, namely

n3) 33 (#T L molecules m&/M

Step 6+ the mean molecular speed is obtained from the *axwell&0oltmann distribution of

gas velocities by integration, yielding

L m sM

where + !& molecular mass L $g M#& 0oltmann constant ( 3 #./ x #9&%/Q BT& temperature L B M

3 /.#1#@

6tep 1 + combining the e'uations from the first three steps gives the >ert&Bnudsenformula for the incident flux

L molecules m&%sM

Note

#. all 'uantities in the above e'uation need to be expressed in 6I units%. the molecular flux is directly proportional to the pressure

0. @as 4xposure - the LangmuirL

"hegas exposureis measure of the amount of gas which a surface has been sub


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"hestic#ing coefficient, S, is a measure of the fraction of incident molecules which adsorbupon the surface i.e. it is a probability and lies in the range 9 & # , where the limitscorrespond to no adsorption and complete adsorption of all incident molecules respectively.In general, Sdepends upon many variables i.e.

S3f ( surface coverage , temperature, crystal face ....

"hesurface coverageof an adsorbed species may itself, however, be specified in a numberof ways +

#. as the number of adsorbed species per unit area of surface (e.g. in molecules cm&%.

%. as a fraction of the maximum attainable surface coverage i.e.

& in which case lies in the range 9 & # .

/. relative to the atom density in the topmost atomic layer of the substrate i.e.

& in which case maxis usually less than one, but can for an adsorbate such as >occasionally exceed one.

Note +

#. whichever definition is used, the surface coverage is normally denoted by the ree$ .

%. the second means of specifying the surface coverage is only usually employed foradsorption isotherms (e.g. the ?angmuir isotherm. "he third method is the mostgenerally accepted way of defining the surface coverage.

/. a !onolayer(# *? of adsorbate is ta$en to correspond to the maximum attainablesurface concentration of adsorbed species bound to the substrate.

e can also as$,

>ow long will it ta$e for a clean surface to become covered with a complete monolayer ofadsorbate 5

"his is dependent upon the flux of gas phase molecules incident upon the surface, theactual coverage corresponding to the monolayer and the coverage&dependent stic$ing


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probability ... however , it is possible to get a minimum estimate of the time re'uired byassuming a unit stic$ing probability (i.e. S3 # and noting that monolayer coverages aregenerally of the order of #9#:per cm%or #9#Gper m%. "hen

Time ? M K 1(#G? F! L s M

Summary- +ariation of *arameters #ith *ressure

!ll values given below are approximate and are generally dependent on factors such astemperature and molecular mass.

Degree of Sacuum8ressure

("orras Density

(molecules m&/ *ean ree 8ath

(m"ime *

(s!tmospheric H@9 % x #9%: H x #9& #9&G

?ow # / x #9%% : x #9&: #9&@

*edium #9&/ / x #9#G : x #9&% #9&/

>igh #9&@ / x #9#@ :9 #Eltra>igh #9 / x #9#% : x #9: #91

e can therefore conclude that the following re'uirements exist for +

Collision ree Conditions 3U 8 J #9&1"orr*aintenance of a Clean 6urface 3U 8 J #9&G"orr

Summary

or most surface science experiments there are a number of factors necessitating a highvacuum environment +

#. or surface spectroscopy, the mean free path of probe and detected particles (ions,atoms, electrons in the vacuum environment must be significantly greater than thedimensions of the apparatus in order that these particles may travel to the surfaceand from the surface to detector without undergoing any interaction with residualgas phase molecules. "his re'uires pressures better than #9&1"orr. "here are,however, some techni'ues, such as IR spectroscopy, which are -photon&inphoton&

out- techni'ues and do not suffer from this re'uirement.(=n a practical level, it is also the case that the lifetime of channeltron andmultiplier detectors used to detect charged particles is substantially reduced byoperation at pressures above #9&@"orr.

%. *ost spectroscopic techni'ues are also capable of detecting molecules in the gasphaseA in these cases it is preferable that the number of species present on thesurface substantially exceeds those present in the gas phase immediately above the


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surface & to achieve a surfacegas phase discrimination of better than #9+# whenanalysing ca. #K of a monolayer on a flat surface this re'uires that the gas phaseconcentration is less than ca. #9#%molecules cm&/ ( 3 #9#molecules m&/, i.e. thatthe (partial pressure is of the order of #9&1"orr or lower.

/. In order to begin experiments with a reproducibly clean surface, and to ensure thatsignificant contamination by bac$ground gases does not occur during anexperiment, the bac$ground pressure must be such that the time re'uired forcontaminant build&up is substantially greater than that re'uired to conduct theexperiment i.e. of the order of hours. "he implication with regard to the re'uiredpressure depends upon the nature of the surface, but for the more reactive surfacesthis necessitates the use of E>S (i.e. J # x #9&G"orr.

It is clear therefore that it is the last factor that usually determines the need for a very goodvacuum in order to carry out reliable surface science experiments.

0.& 4xercises- "he 8ressure Dependence of as 8hase 6urface !dsorption Characteristics

"his section provides a limited number of examples of the application of the formulaegiven in the previous section to determine the +

Density of *olecules in the as 8hase*ean ree 8ath of *olecules in the as 8haselux of *olecules incident upon a 6urfaceRate of !dsorption of *olecules and 6urface Coverages

If you have not already been through 6ection1.%then I would suggest that you stop nowand return to this page only after you have done so

:ithin any one of the folloing sub-sections. it ill be assu!ed that you have already done

the previous &uestions and !ay !a#e use of the ansers fro! these &uestions - you aretherefore advised to or# through the &uestions in the order they are presented0

A. Molecular @as Bensities

hat is the molecular gas density for an ideal gas at /99 B when the pressure is #9&@"orr 5(in molecules m&/

hat therefore would be the gas density at a pressure of #9&G"orr 5

5. Mean ree *ath of Molecules in the @as *hase

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