Thermodynamics: adsorption equilibrium

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Thermodynamicsadsorption equilibrium
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Adsorption

• A large number of scientifically and
  technologically important phenomena are
  fundamentally related to accumulation of chemical
  species or formation of new chemical species at
  the interfaces between different phases.
• Adsorption refers to the SURFACE (of the second
  phase)
• Absorption refers to the BULK (of the second
  phase).
• Hydrogen is adsorbed at the surface of a Pt
  catalyst.
• Carbon dioxide is absorbed by an alkaline water
  solution.

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Types of adsorption
gas/solid, solution/solid, , solid/solid
interface, electrode/electrolyte interface
Approaches
microscopic, classical thermodynamics,
statistical thermodynamics, kinetics of
adsorption and desorption
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Topics
Basic aspects of adsorption (structure of
adsorbed species, structure of interface, nature
of bonds, kinetics of elementary
processes) vacuum technology heterogeneous
catalysis structure of the electrified interface
and kinetics of electron transfer preparation of
ultra pure substances, Environment physical
metallurgy, Materials Science, ... colloid
chemistry
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Gas/solid adsorption
(x, y) indicates the adsorption plane z
indicates the coordinate perpendicular to the
adsorption plane
The molecule is adsorbed on particular sites at
(or near) the surface of the crystal. The
molecule interacts with all atoms (those on the
surface layer and those on the underlying layers).
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The overall interaction between the molecule and
all crystal atoms is described by an overall
potential V(x,y,z)
V(x,y,z) at a particular (x, y), e.g. in front of
a site.
This is the simplest shape to have adsorption
(more complex shapes with more minima are
theoretically predicted and experimentally
verified).
The whole curve changes when other (x, y) are
considered.
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The dept of the potential well can possibly
change this way.

• To discuss the simplest features, we do not need
  a particular knowledge about the nature of the
  molecule - surface bonds.
• Obviously, the nature of these bonds controls
  height, position and curvature of the potential
  well.
• TWO main cases
• V0 gtgt kT localized adsorption
• V0 ltlt kT mobile adsorption

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Langmuir model
It is a simple model for localized
adsorption. There is only one kind of adsorption
sites. On each site, only one molecule can be
bonded. The lattice is not modified by
adsorption. The adsorbed molecule vibrates in a
3D well independently of the vibrations of the
nearby molecules and independently of the
occupancies of the nearby sites (it is an
independent particles model moreover, the role
of the crystal is only to provide adsorption
sites).
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Langmuir model
ST (Statistical Thermodynamics) gives

• N number of adsorbed molecules,
• M number of adsorption sites,
• ? N/M coverage degree
• q q(T) is the partition function of the
  vibration of the molecule in the site

Chemical potential of adsorbed molecules
Chemical potential of gas molecules (P actually
stands for P/Pº)
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Langmuirs isotherm
T const.
J 1
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Langmuirs isotherm

• is an equilibrium constant.
• It is possible to derive Langmuir's equation from
  classical thermodynamics by considering the
  equilibrium
• S(site) A(gas) ? AS(molecule on site)
• If we assume that
• the effective concentration of the adsorbed
  molecules is ? ? and
• the effective concentration of free sites is ?
  (1-?)

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Chemical and physical adsorption
Without dissociation
Chemical adsorption
Physical adsorption
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Chemical and physical adsorption
With dissociation
Chemical adsorption
Physical adsorption
dissociation
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Physical and chemical adsorption
There is a weak interaction (i.e. Van der
Waals), such as that between molecules in a
liquid
There is a true chemical bond between molecule
and site
The molecule-surface distance is long ( a
molecule - molecule distance in a liquid)
The molecule-surface distance is short ( an
atom-atom distance in a molecule)
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Physical and chemical adsorption
Low DH for adsorption ( vaporization enthalpy 5
- 20 kJ/mol
High DH for adsorption ( chemical bond) 40-600
kJ/mol
No dissociation
If possible, there is (usually) dissociation of
the molecule
Adsorption is reversible
Adsorption is not reversible
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Physical and chemical adsorption
(frequently) multi-layer adsorption
Mono-layer adsorption
When P reaches the vapor pressure of the
adsorbing molecules, a liquid is formed on the
surface and ? ? infinity
At high P, ? ? a limiting value
It can be described by Langmuir's isotherm, but
usually other laws are required
(usually) it is well described by Langmuir's
isotherm
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Physical and chemical adsorption
Not specific adsorption is mainly controlled by
the surface area of the solid.
Very specific chemical adsorption typically
requires a particular site (it is possible to see
differences between different crystallographic
orientations)
Usually occurs only at low T
Occurs at variable T (also at high T)
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Physical and chemical adsorption
The adsorption rate is usually very fast
(controlled by the rate of sticking of the
molecules onto the surface, as calculated by the
kinetic theory of gases)
The adsorption rate changes from case to case
No thermal activation
The adsorption rate can be thermally activated
Desorption is always thermally activated
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Physical and chemical adsorption
There is no big difference between adsorbed and
free molecule
Frequently new chemical species are formed their
chemical and spectroscopic properties are
different from those of the free (gas-phase)
molecule
Gives the geometry of the surface (area,
porosity, sometimes also shape of the pores)
Gives information on the chemical nature of the
surface
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Experimental

• Adsorption is experimentally characterized by
  measuring adsorption isotherms, that is
• The amount (m, grams or moles) of the substance
  being adsorbed (per unit mass of adsorbent)
• Against the pressure (or chemical potential) of
  the substance being adsorbed

If one recognizes an asymptotic value (m0), this
is the value corresponding to a monolayer, and
m/m0 directly gives the coverage degree.
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Brunauers types
Type 1 monolayer adsorption
Here, one easily recognizes an asymptotic value
(m0) corresponding to a monolayer.
Type 2 the most frequent multilayer adsorption
Type 3 the least frequent multilayer adsorption
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Hysteresis loops
Brunauers types 4 and 5 are variants of types 2
and 3 with an hysteresis cycle. The lower branch
is sampled on filling, that is with increasing
P. The upper branch is sampled on emptying,
that is with decreasing P the difference is due
to vapor condensation into the pores of the solid
at pressures lower than P0.
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B.E.T. isotherm
The standard tool for modeling experimental
(multilayer) isotherms is BET (Brunauer, Emmet,
Teller) equation c is an empirical parameter,
depends on adsorbent and adsorbate, and measures
the relative strengths of bonds between surface
and first layer and between first and second
layer. The standard way of measuring surface
areas of porous materials is with nitrogen
adsorption at the normal boiling point (P0 1
atm).
x here indicates P/P0 , and P0 is the vapor
pressure of the substance being adsorbed
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B.E.T. isotherm
BET isotherms with different c values.
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