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CLUSTERS:
CHEMISTRY AND
PHYSICS
IN A
FINITE WORLD
TONY STACE
University of Nottingham
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Clusters:
Small collections (~ 1000) of atoms and/or
molecules that are typically studied in the
gas phase. These could behave as extremely
small images of a bulk liquid or solid –
or, they could be unique materials!
How small does the collection have to become,
before it fails to function in the same way as
a bulk material?
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The types of questions we might seek answers
to:
how many water molecules do we need to dissolve
common salt (sodium chloride)?
or
how many metal atoms do we need to make a
piece of copper wire?
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Important physical and chemical
properties of bulk materials:
Structure diamond
Melting ice cube
Conduction of electricity copper wire
Solubility salt in water
Magnetism ???????
Chemistry combustion
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Size effects (bulk): (spherical cluster model)
Ra radius of a single atom
Rc radius of cluster
Volume of 1 atom – 4/3Ra3
Volume of a cluster – 4/3Rc3
no. of atoms (N) is (Rc/Ra)3 Rc = Ra N1/3
Scaling cluster properties: XN = Xbulk(1 β/N1/3) or (1 /R)
Melting temperature of N atoms of gold TM / K = 1336.15 – β/N1/3
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Size effects (surface):
No. of atoms on the surface (Ns) is 4(Rc/Ra)2 = 4N2/3
Fraction of surface atoms Fs = Ns/N = 4/N1/3
Fs < 0.01 (1%) for N > 64,000,000 atoms
The significance of surface atoms is that when Fs is large,
surface energy (surface tension) becomes as important
as bulk binding energy in determining the properties of a
material.
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N Rc(Å) Ns/N (%)
125 4 80
1000* 10 40
10,000 22 10
1m 100 4
* start of nanotechnology
no. of atoms radius atoms on the surface
1 Å = 0.0000000001 m = 0.1 nm
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Production of clusters
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Temperature: 300 K 1 K
Time taken for an atom to reach the vacuum is 0.000001 s
Rate of cooling: >10,000,000 K per second
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Pure argon
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Carbon clusters and fullerenes
Kaldor et al
1984
Kroto et al
1985
How Nobel
Prizes are
won and
lost!!
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Structure
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Be, B, Cd, Co, Ru, Sc, Re
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For clusters, one way to investigate structure
is to look for stable collections of atoms in a
mass spectrum –
- a stable structure will be strongly bound and so will
give a comparatively intense signal.
- structures that are less stable will yield weaker
signals .
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mass spectrum of
clusters produced
from krypton
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All stable icosahedra
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For single-atom systems there is no bulk equivalent – the structure is
only stable because of surface energy.
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The driving force for this effect in small
clusters is surface energy, and a cluster
needs to contain about 2000 atoms before
the bulk binding energy is high enough
for them to adopt stable close-packed
structures.
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Melting
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bulk gold
1,000,000 atoms
10,000 atoms
Melting in deposited gold nanoparticles
TM = 1336.15 – 5543.65/R (Å)
smaller clusters are icosahedra
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Melting is initiated by the presence of mobile
atoms or molecules on surfaces.
On a piece of metal 1cm3 in size, fewer than
0.000000001% of the atoms are on the
surface and so they have almost no influence
on how the metal behaves at low temperature.
However, in a cluster Fs is large and so melting
can take place at much lower temperatures.
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gold nanowires and
the temperatures at
which they fail
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Electrical conductivity
How small is a piece of wire?
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Electrical Properties
hsingle metal atom
e-
ionisation energy
metallic solid
h e-
metal surface
work function ( or )
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work
function
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e-
+
+
+
++
++
+
+
+
+ +
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
None of the electrons are associated with any particular atom
Metal cluster
e-
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Measuring the ionisation energies of mercury clusters
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Ionisation energy of mercury clusters as a function of 1/radius
~100
atoms
single atom
,
Collection of
atoms
Starting to
look metallic
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Solubility
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Sodium chloride (salt) in water
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Entropy is also
important
under certain
circumstances
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Na+ O
H
H
+
+
2-
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Gas phase experiment
Na+ + H2O Na+(H2O) E
Na+(H2O) + H2O Na+(H2O)2 E’
Na+(H2O)2 + H2O Na+(H2O)3 E’’
Na+ + nH2O (E +E’ +E’’ + ....)
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Ion 6 water Bulk
molecules
H+ 1123 1129
Li+ 515 520
Na+ 403 405
K+ 333 321
Ion hydration energies / kJ mol-1
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Na+
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Solvation
For singly-charged metal ions it is possible to
reproduce the essential energetics of ion
solvation with ~ 6 - 10 molecules.
To dissolve sodium chloride we need
approximately 12 water molecule for each
NaCl unit
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No comparable data on how metal ions
carrying more than one charge dissolve.
Almost all of the metals that are
important for our existence and quality
of life carry more than one charge:
Ca2+, Cu2+, Ni2+ and Fe2+/3+
Experiments suggest that these ions
need 20 – 30 water molecules to
dissolve.
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Ca2+
[Ca(H2O)10]2+
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Chemistry
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Ionosphere (100 km)
Most abundant species is NO+
NO originates from activities on the surface of the
Earth and because it has a low ionisation energy,
it acts as a charge sink. Neutral O2 and N2 are far
more abundant, but have much higher ionisation
energies.
As the altitude drops, ions of the form (H2O)nH+
begin to appear and these are thought to be
precursors to cloud formation.
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The clouds that are formed are often referred to
as "night-shining" or Noctilucent clouds.
They form in an upper layer of the Earth’s
atmosphere called the mesosphere during the
Northern Hemisphere’s summer season, and
they are also seen during the summer months in
the Southern Hemisphere.
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Ionosphere (90 km)
Need a chemical route for the transition:
NO+ (H2O)nH+
Suggested pathway:
NO+.(H2O)3 + H2O (H2O)3H+ + HONO
Cluster equivalent
NO+.(H2O)4 (H2O)3H+ + HONO
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2 3 4 5 6 7 8
0
20
40
60
80
100
Decomposition of
NO+(H2O)n clusters
loss of HONO
Rela
tive inte
nsity
n, number of water molecules
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Where is cluster science going?
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Metal clusters and the possibility
of creating new catalysts –
reactions take place on the
surface and clusters offer a high
surface to volume ratio.
Co55
fcc icosahedron
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Helium Nanodroplets
(103 – 106 atoms)
Internal
temperature
of 0.38 K
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Helium nanodroplets (superfluid!):
1 Chemical Reactions at 0.38 K
2) Magnetic behaviour
3) Superconductivity
4) Spectroscopy
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How small is a solid or a liquid?
Structure (regular) ~13 atoms
Structure (bulk) ~2000 atoms
Melting ~1,000,000 atoms
Becoming a metal ~200 atoms
Solvation ~ 6 molecules (Na+)
~ 30 molecules (Cu2+)