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**Gas Adsorption at Solid Surfaces**

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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

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**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: 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. ka Molecules localized = activation barrier hindering migration to adjacent site >>kT, k=boltzmann’s const. kd

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**Langmuir Adsorption Isotherms continued**

In the dynamic equilibrium of associative adsorption: 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. As P 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) 2(M-S) θ = (K’P) / (1 + (K’P) ) where K’ = k’a/k’d 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. k’a k’d 1/2 1/2

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**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 = (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

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**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 [ / 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 [ / T(lnP)]θ = ΔHAD/RT [ln(P1/P2)]θ = (ΔHAD/R)(T1 – T2 ) 2 2 -1 -1

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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. 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.

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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. More vacancy = higher sticking probability While diffusing – losing E, and if E isn’t transferred to solid, it’s likely that molecule will become desorbed (like Langmuir predicts). The longer the molecule is adsorbed, the more likely E will be transferred to surface.

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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”. Ti = Tf = No E exchange

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**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. Fig 1.12

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The Miller Index 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. 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 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) x (111) steps.

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(011) Surface Example

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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. High E surfaces – related to degree of coordination on surface

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**Preparation of Clean Surfaces**

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. Layered cmpds: graphite, mica, some semiconductors Annealing brings impurities to the surface because of the lowered surface E.

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

Maintenance of Clean Surfaces Surface bombardment (Z) by molecules Z = P/(2πMkT) where P is Pambient (Ncm ), 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 torr, and assume worst, S = 1. Z = 3.82 x 10 cm s . If atomic density is typically cm , Z/(cm/ML) = ML/s And for 1 ML = 2.6 s to adsorb at an ambient P However, at 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 torr. 1/2 -2 -6 14 -2 -1 15 10^-6 torr = 1.333x10^-2 N/cm^2. 1 L = 10^-6 torr = 10^-7 torr = 10^-8 torr -10 -6

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**Mobility in Two Dimensions**

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). Write eqn in notes. Diffusivity is related to entropy change b/t equilibrium site and initial site

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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. Incr in MM = incr in vanderWaal interactions

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