Lecture 2—Adsorption at Surfaces 1.Adsorption/Desorption 2.Overlayers, lifting reconstruction 3.Dissociative and Associative adsorption 4.1 st and 2 nd order desorption, kinetics Reading— Lecture on Langmuir adosrption isotherm P. A. Redhead, Vacuum 12 (1962) Smentkowski and Yates, Surf. Sci. 232 (1990) 1

S S SSSS AA A A A Adsorption at open site: S = S 0 No adsorption at occupied site: S = 0 Monolayer Adsorption: Assume an Adsorbate (A) can adsorb at an empty surface site with sticking coefficient S 0. If a surface site is already occupied, then no adsorption occurs (S = 0) 2

(1x1) unit cell 3

Adsorbate forming a (2x2) overlayer on the (1x1) substrate surface 4

Unused surface bonds can interact, causing change in surface structure Surface dimerization 5

Dissociative adsorption of H 2 HHHHHH Adsorption can induce or lift surface reconstructions (e.g., H/Si(100) 6

Associative Adsorption  adsorbate does not break bonds during chemisorption, e.g., CO/W WWWWWW CO 7

WWWWWW HH H2H2 Dissociative adsorption: molecular bonds broken during adsorption 3.g., H 2 on W 8

Consider adsorption (assoc. or dissoc.) at a surface In this process, note that the average sticking coefficient will depend on the fractional surface coverage (Θ). At zero or low coverage, the sticking coefficient will be S 0 : 0<S 0 <1 At Θ = 1 (full coverage), S = 0 For 0<Θ<1, we have S = S 0 (1-Θ) 9

We can therefore model adsorption as an equilibrium between adsorbate, and surface sites: [A] + [S] [AS] Therefore: (1)K ads = [AS]/[A][S] We can then rewrite [AS] and [S] in terms of Θ: (2)[AS]/[S] = Θ/(1-Θ) Given that [A] is some constant (C), we can re- write (1) as K ads = Θ/C(1-Θ), or (3) Θ = K ads C/(1+K ads C) (the usual form for the Langmuir Isotherm) 10

(3) Allows us to determine the fractional surface coverage as a function of C (typically proportional to pressure) For small C, K ads C << 1, and Θ ~ K ads C For large C, we have K ads C >> 1 And Θ ~ 1 Θ C Θ~ K ads C Θ~1 11

In many laboratory situations, adsorption at a given temperature is, for all practical purposes, irreversible. K ads is very large, and the equilibrium fractional surface coverage is 1. However, we are often concerned with the kinetics of coverage, as we can control the total exposure of a gas to the surface. Assuming that once adsorbed at a given temperature, A will not desorb, we have Θ = SFt where S = sticking coefficient, F = flux to the surface (suitably normalized, and proportional to pressure), and t = time. Ft = “exposure”. Typically, exposure is measured in “Langmuirs” (L) where L = Torr-sec 12

Note, however, the S is not constant. We have S = S 0 (1-Θ) We then have : (4) Θ = S 0 (1-Θ)cPt where c is a constant, and P = Pressure Differentiating both sides of (4) with respect to t, (5) dΘ/dt = S 0 cP – S 0 cP(dΘ/dt) For Θ << 1, we have dΘ/dt ~ S 0 cP, and coverage will increase linearly with exposure For Θ ~ 1, (6) then dΘ/dt = 0, and coverage is constant with time 13

Θ P x t 14

Interrogating adsorption and desorption  Temperature Programmed Desorption (TPD)  Temperature Programmed Reaction Spectroscopy (TPRS) Typical experimental apparatus (Gates, et al., Surf. Sci. 159 (1985) 233 Typically need: QMS with line of site Controlled dosing Temperature control with linear ramp Another method to monitor surface composition/structure (Auger, XPS, LEED…) 15

TPDStep 1: Adsorption at Low Temp Step 2: Desorption vs. temperature: dT/dt ~ 1-10 K/sec QMS 16

1 st and 2 nd order desorption 1 st order, desorption occurs from a surface site 2 nd order, desorption occurs after surface reaction and combination, e.g.; H ads + H ads  H 2 desorbed 17

In monitoring desorption from a surface, the desorption rate (N(t); molecules/cm 2 -sec) is proportional to two pressure-dependent terms (see Redhead) aN(t) = dp/dt + p/λ a = constant (dependent on surface area) p = pressure λ = pumping time (reciprocal of pumping rate) In modern vacuum systems, λ is very small, and p/λ becomes the dominant term. The desorption rate is therefore proportional to the (partial) pressure as measured by the QMS: N(t) = kp 18

We can therefore monitor the desorption rate by looking at the change in partial pressure of the desorbing species (e.g., H 2, CO, etc.) in the QMS: P CO T ( = T 0 + βt)  Temperature of desorption rate maximum 19

We can (Redhead) express N(t) as the product of an Arrhenius rate equation: (7) N(t) = -dѳ/dt = v n ѳ n exp(-E/RT) v = rate constant n = order of the reaction ѳ = concentration of adsorbates (molecules/cm 2 ) E = activation energy 20

Given that T = T 0 + βt (the linear heating rate is critical), we can solve (7) for the temperature at which N(t) is a maximum (T = T P ) (Redhead, again) For n = 1 (1 st order) (v 1 is the first order rate constant) (8a)E/(RT p 2 ) = ( v 1 /β)exp(-E/RT p )  T P independent of surface coverage (note: this assumes E does not vary with surface coverage; not always true) For n = 2 (2 nd order) (8b) E/RT P 2 = (σ 0 v 2 /β)exp(-R/T P )  T P is a function of initial surface coverage (σ 0 ) 21

From 8a, b, we can see that one way to distinguish 1 st from 2 nd order desorption processes is to due the same desorption expt at different surface coverages: Initial coverage, 0.7 ML Initial coverage, 0.4 ML 1 st order reaction, temp. of peak maximum is invariant with initial coverage. 22

2 nd Order : Peak temperature decreases with increasing initial coverage (desorption of H 2 from W: Redhead) 23