Surfaces
Gas Adsorption
at Solid Surfaces
Definitions
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Adsorption: A molecule (adsorbate) that forms a
bond to the surface (adsorbent).
Associative Adsorption: A gas molecule adsorbs
without fragmentation.
Dissociative Adsorption: A gas molecule adsorbs
and fragmentation occurs.
Fractional coverage of adsorbate (θ)
NS

N
where Ns = number of surface sites occupied by
adsorbate and N = total number of substrate
adsorption sites
–
When θ = 1, a monolayer exists
Langmuir Adsorption
Isotherms
Adsorption Isotherm: θ depends on, and is linearly related
to, pressure (P) at a constant temperature (T). This
relationship is used to look at equilibrium adsorption
behavior, and to find the total surface area of a substrate
(SA), but the following assumptions must be made:
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–
–
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1: The solid surface is uniform and each site (all are equivalent)
can be occupied by 1 molecule.
2: A dynamic equilibrium exists between the gas (at P) and the
adsorbed layer at constant T. For associative adsorption: M(g)
ka
+ S(surface site) M-S (ka and kd are the rate constants of
kd
adsorption and desorption, respectively)
3: Adsorbates (g) continually collide with the surface. Upon
impact of a vacant site, the adsorbate sticks. Upon impact of a
filled site, they are reflected back into the gas phase.
4: Once adsorbed, molecules are localized and the enthalpy of
adsorption (ΔHAD) per site is constant, independent of θ.
Langmuir Adsorption Isotherms
continued
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In the dynamic equilibrium of associative adsorption:
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RateAdsorption = kaP(1- θ) = RateDesorption = kdθ
Upon rearrangement, we see that θ = NS/N = KP/(1+KP), where
K = ka/kd. We can predict how θ changes with P.
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
0, θ = 0 and as P
, θ = 1. If KP<<1, θ = KP.
In the dynamic equilibrium of dissociative adsorption:
–
M2(g) + 2S(surface site)
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As P
k’a
k’d
2(M-S)
θ = (K’P) / (1 + (K’P) 1/2 ) where K’ = k’a/k’d
1/2
Since NS is hard to determine, mass and volume may be
used to find θ: θ = m/m = V/V, where m & V are the
mass and volume of the adsorbed gas at constant P, and
m & V are the mass and volume corresponding to all
substrate sites being occupied. If N, m or V is known,
SA can be calculated.
Langmuir Adsorption Isotherms
continued
Surface area, SA = N*Am, where Am = areamolecule and
N can be calculated using m:
m/M = nM = total # of moles in 1 monolayer (ML)
nM = N/L, where L = Avogadro’s number
so N = (mL)/M, where M = molar mass
or N can be calculated using V:
PV = nMRT (at constant P & T), so
N = (PVL)/RT
And SA as specific surface area = SA/mass of
substrate
Heats of Adsorption
Adsorption of gas on a solid is exothermic.
ΔHAD is the isoteric (constant θ) enthalpy of adsorption.
Determining the thermal energy evolved when a known
amount of gas is allowed to adsorb onto a clean
surface (T rise of solid) can help to derive ΔHAD.
ΔG° = -RTlnK° = ΔH°AD – TΔS°AD
lnK° = ΔH°AD/RT + ΔS°AD/R
Differentiate with respect to T at constant θ
2
[ / T(lnK°)]θ = ΔH°AD/RT
Remember: KP = θ/(1-θ)
lnK + lnP = ln(θ/(1-θ)
[ / T(lnK)]θ + [ / T(lnP)]θ = 0
[ / T(lnK)]θ = [ / T(lnK°)]θ
2
[ / T(lnP)]θ = ΔHAD/RT
-1
-1
[ln(P1/P2)]θ = (ΔHAD/R)(T1 – T2 )
Adsorbate Bonding
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Physisorption: Adsorbate/Adsorbent bonding
interaction is long range, weak,and reversible,
associated with van der Waal interactions. There is a
negligible exchange of electrons and a surface
potential at the interface between two phases – gas
and solid – where an “overspill” of electron charge from
the solid into the gas phase results in an imbalance of
electron density.
Chemisorption: An exchange of electrons between
absorbate and adsorbent occurs, associated with
covalent, ionic and metallic bonding. The ΔHAD is
larger than that of physisorption. As chemisorption
proceeds, defects in ordered arrays and closer
proximities of adsorbates destabilize the adsorbed
layer, and this is seen in ΔHAD.
Kinetics
Sticking probability (S) is the probability of a molecule being
associatively adsorbed from the gas phase into a
chemisorbed state assuming Langmuir behavior.
S = S0(1-θ) where S is the rate of adsorption of adsorbates
over the rate of collision of molecules with the surface (Z),
and S0 is the sticking probability at θ = 0.
Sometimes S is larger than predicted using Langmuir
isotherm because if a molecule hits a filled site, it could
form weak Van der Waal interactions with the surface,
diffuse, and then move to a vacant spot where it will
become chemisorbed. If adsorbate is initially physisorbed
to a vacant site, it is referred to as an intrinsic precursor
state, while if it is physisorbed to a filled site, it is an
extrinsic precursor state.
Kinetics continued
The rate at which molecule collide with the
surface is measured by a thermal
accommodation coefficient (α)
α = (Tf – Ti)/(Ts – Ti)
where Ti is the Tinitial of the molecule in the gas
phase, Tf is the Tfinal of the molecule after
collision with the surface, and Ts is the Tsurface.
When Ti = Tf, α = 0 and the molecules are
elastically scattered.
When Ts = Tf, α = 1 and the adsorbates are all
“accommodated”.
Well-Defined Surfaces
In order to make surfaces more comparable,
controlled amounts of defects are added to
surfaces. Typically, single crystal surfaces are
used – cut using X-ray back
scattering so that a particular
crystal plane is exposed. The
surfaces are then flat, with
mostly large terraces, or vicinal,
with short, flat terraces that are
separated by atomic steps.
The Miller Index
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The Miller index is used for notation of the crystal planes
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(x,y,z) for simple cubic, face centered cubic (fcc), or body centered
cubic (bcc)
(w,x,y,z) for hexagonal close packed surfaces (hcp)
Rules
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Find where the plane intersects the x, y, and z axes in multiples of
unit cell dimensions (a)
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 is used for a plane parallel to an axis, and –1 is written as Ī
Take the reciprocal of the numbers
If fractions result, make the ratio into whole numbers.
Example: A plane that runs parallel to the x-axis, but intersects the
y- and z-axes at 1: , 1, 1 becomes (011).
Planes with a high Miller index are not flat, but have narrow planes
separated by steps and are described with the following
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n(x,y,z) x (u,v,w), where n = the average number of atoms on a
terrace, (x,y,z) is the Miller index of the plane and (u,v,w) is the Miller
index of the step.
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fcc: (331) = 3(111) x (111), which is 3-atom wide (111) terraces separated
by (111) x (111) steps.
(011) Surface Example
Surface Relaxation
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Atoms in (111), (100), and (110) fcc have lost 3, 4 or 5
nearest neighbors of the original 12 and to compensate
for the loss of bonding, the surface will relax, which is
an oscillatory change in interplanar spacing (Δd).
During surface relaxation, the 1st layer of atoms
contracts towards the 2nd layer to increase coordination,
and the 3rd layer reacts by expanding away from the 2nd
layer. This continues until 5 or 6 layers deep (the
selvedge) until the oscillations are damped.
The largest relaxation occurs in high energy surfaces
with low atomic density.
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In fcc, (110) > (100) > (111)
In bcc (111) > (100) > (110)
If the energy is large enough, the plane could
reconstruct to enhance coordination of surface atoms
and to lower the energy of the surface.
Preparation of Clean Surfaces
Cleaning the surface
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Layered compounds (graphite, mica and some
semiconductors) can be cleaved
Metal catalysts can be rid of excess oxygen by heating
the sample in the presence of hydrogen.
Sputtering cleans the sample using high energy argon
ions to bombard the surface. The energy transfer from
the ions breaks bonds of the surface and adsorbates,
but leaves the surface rough, so it is best to anneal the
surface to flatten it after sputtering. Sputtering and
annealing should be repeated several times because
annealing the sample can bring impurities from the
bulk to the surface.
Maintenance of Clean Surfaces
Surface bombardment (Z) by molecules
1/2
Z = P/(2πMkT)
where P is Pambient (Ncm-2 ), M is in units of (kg/molecule), T is
in Kelvin, and k is Boltzmann’s constant (J/K). The rate of
contamination also depends on a molecule’s sticking
ability.
Example: CO – 300K, P = 10 -6 torr, and assume worst,
14
-2 •-1
S = 1. Z = 3.82 x 10 cm s . If atomic density is typically
1015 cm ,
Z/(cm/ML) = 0.382 ML/s
And for 1 ML = 2.6 s to adsorb at an ambient P
-10
However, at 10 torr, it takes 7.3 hours for 1 ML to adsorb,
so an ultra high vacuum is necessary to keep surfaces
clean.
Langmuir units (L) are used to describe gas exposures, and
the definition is an exposure for 1 second at 10 -6 torr.
Mobility in Two Dimensions
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Surface Diffusion: atoms and molecules are
mobile to equilibrate and minimize free energy
states.
The rate of diffusion is dependent on the direction
in which the diffusion occurs, T and θ.
Physisorbed molecules have low ΔH°AD and low
diffusion activation energies and therefore are
very mobile in ambient T.
Chemisorbed molecules, on the other hand, are
immobile in ambient T, because of higher
activation energies.
The activation energy is larger for rough surfaces
than for smooth surfaces. For the rate of
diffusion: Stepped < (100) < (110) < (111).
Lateral Interactions
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Direct Coulombic: (alkali metals) adsorbates and either
adsorbent or oppositely charged adsorbates transfer
charge and become co-adsorbed.
Direct Covalent/Metallic: (transition metals) two
adsorbates with partially filled valence orbits bond together
Van der Waal: (self-assembling ML (SAM)) distortions of
adsorbate’s electron density induces a temporary dipole
moment in a neighboring adsorbate. These interactions
are dominant in non-polar, large molecules.
If substrate/adsorbate interactions are greater than
adsorbate/adsorbate interactions, the overlayer is referred
to as “commensurate” and the interadsorbate spacing is
equal to the substrate/adsorbate spacing or a multiple.
If substrate/adsorbate interactions are similar to
adsorbate/adsorbate interactions, the overlayer is referred
to as “incommensurate”, and the spacing may not be a
multiple, and a wide range of sites will be occupied.