Surfaces – Gas adsorption at solid surfaces. 1/28/13. 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
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where Ns = number of surface sites occupied by adsorbate and N = total number of substrate adsorption sites
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
[ /T(lnK°)]θ = ΔH°AD/RT2
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 )
In order to make surfaces more comparable, controlled amounts of defects are added to surfaces. Typically, single crystal surfaces areused – aligned using X-ray back scattering then polished so that a particularcrystal plane is exposed. The surfaces are then flat, with mostly large terraces, or vicinal, with short, flat terraces that areseparated by atomic steps.
Flat = large terraces
Vicinal = small terraces with many steps
Axes in unit cell dimensions
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)
Cleaning the surface
Surface bombardment (Z) by molecules
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 = 10-6torr, 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 10-10torr, 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.
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:
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 = (mL)/M, where M = molar mass
or N can be calculated using V:
PV = nMRT (at constant P & T), so
N = (PVL)/RT
And SA as specific surface area = SA/mass of substrate
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”.