ChE 553 Lecture 11

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ChE 553 Lecture 11

• New Topic Kinetics Of Adsorption

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Objective

• Start to Look at rates of adsorption
• Qualitative features
• Models

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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

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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

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Definitions

• Scattering, trapping, sticking

Figure 5.1 A schematic of the processes that can
occur when a molecule collides with a solid
surface.
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Definitions

• Elastic Scattering
• Inelastic Scattering
• Trapping
• Sticking

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.
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Physics Of Trapping

1. Molecule comes in and hits the surface.
2. Loses energy, so the molecule no longer leaves
   the surface.

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.
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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.

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.
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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

Knudsen's experiments of the temperature of
flames near surfaces.
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The Thermal Accommodation Coefficient

• Ein incident energy
• Eout exiting energy
• Es energy if molecule accommodated with the
  surface
• ?1 implies that the temperature of a desorbing
  molecule equals the surface temperature
• ? O implies Ein Eout

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Baules Model For Accommodation Coefficients

• Assume molecules behave like billiard balls
• Use material from freshman physics to calculate
  how much energy is transferred during collisions

Figure 5.3 A diagram of the collision between a
hard sphere adsorbate molecule and a hard sphere
surface atom.
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Lots Of Algebra Yields

(5.10)
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Weinberg-Merrill Model For Trapping Probabilities

• Molecule
• Gains W
• Loses energy when it collides with atomic cores
  assume given by Baule result
• Bounces

Does molecule have enough energy to leave? (need
to have more energy than W after collision)
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Result Molecule Will Be Trapped Whenever

• (5.13)
• Algebra yields
• (5.17)

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Masel-Weinberg-Merrill Ion Cores In Jellium Model
Figure 5.5 A schematic of all idealized jellium
potential over a closed packed metal surface.
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Comparison To Data
Figure 5.7 A comparison of the trapping
probability for Xe on Pt(111) (a) Equation
5.26, with ms 195 AMU, w 8 kJ/mole (b)
Arumainayagam et al.s 1990 data and Langevin
results.
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Key Prediction Of Model
Figure 5.9 A plot of Equation 5.26 as a function
of mg/ms for Eicos2(?i)/w 0.1, 0.5, 1, 2, 5,
10.
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 mg/ms.
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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.

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

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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

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Rate Determining Step Different In Trapping And
Sticking

• Trapping - energy transfer is rate determining
  step - a gas surface collision only last 10-13
  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 10-6 sec. There is much more time for
  energy transfer, so molecule thermally
  equilibrates with the surface. Rate determined
  by whether particles stick.

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Recall Langmuirs Model Of Adsorption

Figure 12.34 A plot of the rate of the reaction
A?C calculated from Equation (12.143) with k40,
PB 0, 1, 2, 5, 10 and 25., KA KB 1.
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Sticking Probability

(5.40)
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Rate Of Adsorption

• The rate of adsorption, ra, is related to the
  sticking probability by
• where is the total flux of molecules onto the
  surface in molecules/cm2 sec.
• From kinetic gas theory

(5.41)
(5.43)
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Practical Exposures Measured In Langmuirs

• 1L 1 second exposure at 10-6 torr pressure
•  
• 1 torr 1/760 atm.
•  
• Corresponds to 3x1014 molecules of CO, 2x1015
  molecules of H2 (H2 moves faster than CO)

(5.44)
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Sticking Probability Can Be Made By Measuring
Coverage vs Exposure And Differentiating

(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.)
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Summary

• Trapping and Sticking
• Trapping rate determined by energy accommodation
• Bautes model related
• Sticking rate determined by finding bare sites