Surfaces – Gas adsorption at solid surfaces

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Why Surfaces?• Heterogeneous catalysts are solids

– Solid surfaces can immobilize catalyst particles• Reactions occur at interfaces

– Liquid/solid– Gas/solid

• Atoms in the surface are under-coordinated compared to bulk atoms– Fcc bulk = 12 bonds

• (111) = 9• (100) = 8• (110) = 6

– More reactive compared to the bulk• On the nano-scale, surfaces become more

important because higher surface : volume ratio

Definitions• 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)

where Ns = number of surface sites occupied by adsorbate and N = total number of substrate adsorption sites– When θ = 1, a monolayer exists– θ = occupied sites, 1-θ = free sites

N

N S

Heats of Adsorption• Adsorption of gas on a solid is exothermic.

– Microcalorimetry a technique that measures heat given off due to molecular 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/RDifferentiate with respect to T at constant θ

[ / T(lnK°)]θ = ΔH°AD/RT2

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A(g ) + S↔K

A − S S = surface site

Remember: KP = θ/(1-θ)lnK + lnP = ln(θ/(1-θ)

[ / T(lnK)]θ + [ / T(lnP)]θ = 0[ / T(lnK)]θ = [ / T(lnK°)]θ

[ / T(lnP)]θ = ΔHAD/RT2

[ln(P1/P2)]θ = (ΔHAD/R)(T1 – T2 ) • Isosteric (constant coverage) enthalpy of

adsorption can be determinedP2 P1

T1T2

Adsorbate Bonding• 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. (ΔH° <35 kJ/mole

• 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 causing disorder, and this is seen in ΔHAD.

Kinetics• Hertz-Knudsen equation

– Flux of molecules

• 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.

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ZW =p

2πmkBT( )1/ 2

Well-defined SurfacesIn order to make surfaces more

comparable, controlled amounts of defects are added to surfaces. Typically, single crystal surfaces are used – aligned using X-ray back scattering then polished 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.Flat = large terraces

Vicinal = small terraces with many steps

Miller Indices• The Miller index is used for notation of the crystal planes

– (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

– Find where the plane intersects the x, y, and z axes in multiples of unit cell dimensions (a)• 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.– Planes with a high Miller index are not flat, but have narrow planes

separated by steps and are described with the following• 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.– fcc: (331) : 3(111) x (111), which is 3-atom wide (111) terraces separated by

(111) steps.

ExamplesZ

Y

X

Intercepts = 2, 3, 4

Reciprocal = 1/2, 1/3, 1/4

To get Miller index multiple by least common denominator (12)Miller Index = (6,4,3)

Axes in unit cell dimensions

Example: A plane that runs parallel to the x-axis, but intersects the y- and z-axes at 1: , 1, 1 becomes (011).

Stereographic Triangle• Every Miller Index is combination of (111), (100) and(110)

– Width of terrace; facets of terrace, step edge, and kink sites• Stereographic Triangle is a 2D representation of 3D space –

Highlights all surfaces of 1 handedness• If Miller index “looks” like a high symmetry surface, the

terraces are of that facet i.e – (10,10,9) has (111) terraces.• Chiral Miller index (hkl) defined as h ≠ k ≠ l ≠ 0

• Chirality of surface denoted by direction of decreasing density of microfacets• (111) > (100) > (110)• CW = R CCW = S

• (111) = 1 specific face• {111} = set of equivalent

faces• [111] = 1 specific direction• <111> = set of equivalent

directions

Surface Explorer

• http://surfexp.fhi-berlin.mpg.de/• Allows input of any Miller Index to visualize

the surface

Surface Relaxation• 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.– 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.Au 22x√3 (110) Si(111) 7x7

Preparation of a Clean Surface

Cleaning the surface– 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 a Clean Surface

Surface bombardment (Z) by moleculesZ = 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, S = 1. Z = 3.82 x 1014 cm-2 s-1 . If atomic density is typically 1015 cm2 ,

Z/(cm/ML) = 0.382 ML/s

And for 1 ML = 2.6 s to adsorb at an ambient P

However, at 10-10 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.

Dosing Molecules• Unit of exposure = Langmuir (L)

– 1 L = 1 x 10-6 torr*sec (1.3 x 10-6 mbar*sec)– 0.01 L = 1 x 10-8 mbar * 1 sec– 0.05 L = 1 x 10-8 mbar * 5 sec– 0.05 L = 5 x 10-8 mbar * 1 sec– 0.12 L of MeOH at 30 K, 100 L of O2 at RT, 103 L of H2 onto Pd/Cu(111) at RT

• To compare Langmuirs to coverage (θ ML), need to do STM or spectroscopy• When comparing Langmuir doses of different molecules need to account for

ionization cross-section– NIST website (http://physics.nist.gov/PhysRefData/Ionization/Xsection.html)– Assume 100 eV to compare

Mobility in 2 Directions

• 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. (1/3 of Desorption Energy)

• 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 < (110) < (100) < (111).

Lateral Interactions

• 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.

Langmuir Adsorption IsothermsAdsorption 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:

ka

kd

– 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) + S(surface site) M-S (ka and kd are the rate constants of 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.

Low P

θ

Langmuir Adsorption Isotherms continued

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=NSN=KP

1+KPK =

kakd

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 numberso N = (mL)/M, where M = molar mass

or N can be calculated using V:

PV = nMRT (at constant P & T), soN = (PVL)/RT

And SA as specific surface area = SA/mass of substrate

Langmuir Adsorption Isotherms continued

Kinetics

The rate at which molecule collide with the surface and lose energy to become adsorbed 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”.

King and Wells to Determine Sticking Coefficient

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s(t) =po − p(t)

po − pb

time

pressure