ChE 553 Lecture 12 Theory Of Sticking 1

Objective Develop a qualitative understanding of sticking Go over some models for the process 2

Topics For Today Definition of sticking probability Types of sticking vs coverage Langmuir’s model Precursor model Immobile adsorption 3

Review: Trapping Vs Sticking Trapping Lose enough energy to go below the zero in potential Can easily desorb Sticking Lose enough energy to fall into the bottom of the well Desorption much harder 4

Rate Determining Step Different In Trapping And Sticking Trapping – energy transfer is rate determining step – a gas surface collision only last sec so need to transfer energy quickly Sticking – finding an empty place on the surface to bond to is rate determining step – once trapped molecule stays on the surface for at least sec. There is so much more time for energy transfer, so molecule thermally equilibrates with the surface. Rate determined by whether particles stick. 5

Sticking Probability The rate of adsorption, r a, is realted to the sticking probability by Where is the total flux of molecules onto the surface in molecules/cm 2 sec. 6 (5.40) (5.41)

Sticking Probability Varies With Adsorbate Trapping probability Coverage/number of bare sites Type of Adsorption –Molecular or dissociated Mobility of adsorbed layer 7

Variation In Sticking Probability With Coverage 8 Figure 5.14 A general classification of the variation in the sticking probability with coverage. (Adapted from Morris et al. [1984].)

Type A Behavior Curve A shows the simplest behavior: a linear drop in the sticking probability with coverage. Sticking probabilities drop with increasing coverage because the adsorbate takes up sites. If another adsorbate molecule comes in and hits the filled sites, the new adsorbate molecule cannot stick; instead it desorbs. Type A: Not usually observed. 9

Type B Behavior Type B behavior in non-linear drop in the sticking probability with increasing coverage. Curvature in the sticking can arise for different reasons. If the adsorbate dissociatively adsorbs so it blocks two or more sites. Strong adsorbate/adsorbate interactions. Variation in the heat of adsorption with coverage. Immobile adsorbates. Type B behavior is quite common. 10

Type C Behavior Type C behavior is when the sticking probability is nearly constant up to some intermediate coverage and then drops at higher coverages. Type C behavior arises when the incoming molecules are initially trapped into a weakly bound ”precursor” state. The molecules then move around the surface and find a site to adsorb. Type C behavior also arises when adsorbate layer is mobile. 11

Type D Behavior Type D behavior occurs when the sticking probability initially drops with increasing coverages, then rise again. Type D arises in systems that show a phase transition. One phase adsorbs more strongly than another. Surface reconstructions are a common phase transition. 12

Type E Behavior Type E behavior – the sticking probability initially rises as one adsorbs gas. Probability drops as one fills up sites. Experimentally, type E behavior occurs mainly in trapping-dominated systems and in other systems where energy transfer plays an important role. 13

Type F Behavior Multiple plateaus and dips. Common on polycrystalline samples 14

Sticking Probability Also Varies With Gas Temperature, Incident Energy 15 Figure 5.15 The initial sticking probability of hydrogen on a Ni(111), Ni(110), Cu(111), Pt(110) Ф i = 10˚ and 60˚ as a function of the energy of the incident gas. (Data of Rendulic and Winkler [1989].)

Theories Of Sticking Langmuir’s Model Precursor Model –Equation also works for mobile adsorption Immobile adsorption 16

Langmuir’s Model 17 (5.46) (5.47) (5.48) Figure A plot of the rate of the reaction A  C calculated from Equation (12.143) with k 4 =0, P B = 0, 1, 2, 5, 10 and 25., K A = K B =1.

Langmuire Model Limited Only explains type A&B behavior. In reality, species can be trapped and move around to find sites. Adsorbates interact. These interactions are not included in the Langmuir analysis. 18

Precursor Model Precursor model Gas phase molecules trapped into a precursor state Move around Can stick when over a bare site Can move atoms out of the way when over and empty site 19

Model Equations A FI =precursor over a filled site A MT =precursor over an empty site 20 Figure 5.16 The precursor mechanism for nondissociative adsorption.

Pages of Algebra Give Very Complex Equation 21 (5.59)

Simplification If sticking of AFI negligible (5.60) Sticking higher than Langmuir’s 22

Immobile Adsorption Molecules stick when they land on a bare site Do not stick elsewhere Leads to variation from Langmuir when molecules adsorb on more than one site 23

Saturation Coverage Can Be Less Than Full Coverage Because Isolated Sites Cannot Adsorb Gas 24 Figure 5.18 Some of the arrangements formed with immobile dimers on a square surface. (a) Bare surface. (b) One dimer. (c) Two dimers. (d) Saturated surface.

Approximation: Roberts & Miller 25

Roberts & Miller Predicts Higher Initial Sticking Than Langmuir i.e. (5.80) Works at low concentrations 26

Why Higher Sticking Prob? 27 F igure 5.19 Site blocking by (a) two adjacent atoms, and (b) two atoms that separate.

Saturation Density Less Than Unity For random adsorption on two adjacent sites Vette’s approximation 28

Summary Sticking determined by ability of molecules to find sites Sticking varies with T and  S(0) approximated by ion cores in jellium S(  ) three models –Langmuir –Precursor/mobile –Immobile 29