ChE 553 Lecture 11 New Topic: Kinetics Of Adsorption 1

Objective Start to Look at rates of adsorption –Qualitative features – Models 2

Topics  Definitions of scattering, trapping, sticking  Theory of trapping  Role of thermal accommodation  Models: hard spheres, ion cores in jellium, spring models  Introduction of sticking  Definition of sticking probability 3

What Occurs When A Molecule Sticks? Molecule attracted to surface Hits surface –Too much momentum to stick Loses excess energy and momemtum Diffuses along surface until it finds a place with strong binding Rate usually determined by Mass transfer – how often do molecules collide Energy and momentum transfer 4

Definitions Scattering, trapping, sticking 5 Figure 5.1 A schematic of the processes that can occur when a molecule collides with a solid surface.

Definitions Elastic Scattering Inelastic Scattering Trapping Sticking 6 Figure 5.2 A series of trajectories seen when a molecule collides with a surface. The trajectories were calculated with the computer program in Examples 5.C and 5.D.

Physics Of Trapping a)Molecule comes in and hits the surface. b)Loses energy, so the molecule no longer leaves the surface. 7 Figure 5.2 A series of trajectories seen when a molecule collides with a surface. The trajectories were calculated with the computer program in Examples 5.C and 5.D.

Basic Theory Of Trapping Calculate how much energy the molecule loses as it collides with the lattice. Does it lose enough to fall into the well. 8 Figure 5.4 The potential energy seen by a normal incidence molecule when it collides with a solid surface. A series of lines is shown because the potential is different when the incoming atom hits at different places along the surface.

Need To Understand Energy Flow In Gas Surface Collisions To Proceed Key concept (Baule) – temperature discontinuity when gases interact with surface Implication – when a molecule collides with a surface, it exchanges some but not all of energy with the surface If molecules hotter then surface they cool If molecules cooler than surface they heat 9 Knudsen's experiments of the temperature of flames near surfaces.

The Thermal Accommodation Coefficient E in = incident energy E out = exiting energy E s = energy if molecule accommodated with the surface  =1 implies that the temperature of a desorbing molecule equals the surface temperature  =O implies E in = E out 10

Baule’s Model For Accommodation Coefficients: Assume molecules behave like billiard balls Use material from freshman physics to calculate how much energy is transferred during collisions 11 Figure 5.3 A diagram of the collision between a hard sphere adsorbate molecule and a hard sphere surface atom.

Lots Of Algebra Yields 12 (5.10)

Weinberg-Merrill Model For Trapping Probabilities Molecule 1)Gains W 2)Loses energy when it collides with atomic cores – assume given by Baule result 3)Bounces 13 Does molecule have enough energy to leave? (need to have more energy than W after collision)

Result: Molecule Will Be Trapped Whenever (5.13) Algebra yields (5.17) 14

Masel-Weinberg-Merrill Ion Cores In Jellium Model 15 Figure 5.5 A schematic of all idealized jellium potential over a closed packed metal surface.

Comparison To Data 16 Figure 5.7 A comparison of the trapping probability for Xe on Pt(111): (a) Equation 5.26, with m s = 195 AMU, w = 8 kJ/mole; (b) Arumainayagam et al.’s [1990] data and Langevin results.

Key Prediction Of Model 17 Figure 5.8 A plot of the trapping probability predicted by Equation 5.26 as a function of the incident energy of the molecule for various vales of m g /m s. Figure 5.9 A plot of Equation 5.26 as a function of m g /m s for E i cos 2 (Ф i )/w = 0.1, 0.5, 1, 2, 5, 10.

Model Works Well On Metals, Not As Well On Insulators Reason: metals – atoms cores move separately Insulators – atom cores are bumping up against each other – you cannot move one atom, you have to move several atoms In effect the mass that you have to move goes up so energy transfer goes down. 18

Zwanzig-Ehrlich Model: 19 Figure 5.10 Zwangig’s [1960] model of the interaction of a gas molecule with a one-dimensional chain of surface atoms. Figure 5.12 The critical energy for trapping. (Adapted from calculations of McCarroll and Ehrlich [1963].) (5.31) Never seen experimentally - reason atoms not connected by springs.

Summary Of Trapping: Rate determined by how energy lost during collisions Larger well depths increase trapping Lighter adsorbates decrease trapping Hotter surfaces decrease trapping Heavier surface atoms decrease trapping Stiffer surfaces decrease trapping 20

Trapping And Sticking Are Similar 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 21

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 and 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 much more time for energy transfer, so molecule thermally equilibrates with the surface. Rate determined by whether particles stick. 22

Recall Langmuir’s Model Of Adsorption 23 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.

Sticking Probability 24 (5.40)

Rate Of Adsorption The rate of adsorption, r a, is related to the sticking probability by where is the total flux of molecules onto the surface in molecules/cm 2 sec. From kinetic gas theory 25 (5.43) (5.41)

Practical Exposures Measured In Langmuirs 1L = 1 second exposure at torr pressure 1 torr = 1/760 atm. Corresponds to 3x10 14 molecules of CO, 2x10 15 molecules of H 2 (H 2 moves faster than CO) 26 (5.44)

Sticking Probability Can Be Made By Measuring Coverage vs Exposure And Differentiating 27 (5.45) Figure 5.13 The amount of carbon monoxide that sticks on a Pt(410) surface as a function of the carbon monoxide exposure. (Data of Banholzer and Masel [1986].)

Summary Trapping and Sticking Trapping rate determined by energy accommodation –Baute’s model related Sticking rate determined by finding bare sites 28