PART TWO
PHYSICAL CHEMISTRY AND NANOSCIENCE: INTRO
Everything you've learned in school as "obvious" becomes less and less obvious as you
begin to study the universe. For example, there are no solids in the universe. There's not
even a suggestion of a solid. There are no absolute continuums. There are no surfaces.
There are no straight lines.
R. Buckminster Fuller
US architect & engineer (1895 - 1983)
14-1
NANOSTRUCTURES: Importance of the Surface
One of the principal physical differences between nanostructures and bulk (macro)
structures is that there is a large number of ions/atoms/species on the surface
of a nanostructure
We say that the surface to bulk ratio is large
For an infinite array we say the bulk/total ratio
1
Three factors that relate to surface area will
be explored:
1. Effect of subdivision of parent material
2. The effect of particle shape on surface
Area
3. Surface to Volume Ratio trend with
particle size
Surface area has increased
14-2
Surface Areas: More
Collective surface area and surface to volume ratio are inversely proportional to
The size of the particle
Collective Surface Area: Sum total of surface Areas of individual nanoparticles
- Extensive property-
Surface-to-volume ratio: S/V for one particle or like particles
-Intensive property
S/V usually is quoted without units
14-3
Consider Spherical atoms/Ions/nanoparticles
Volume of a sphere
Surface Area
So as r decreases the proportion of surface wrt to bulk increases
In the collective sense the total surface area increases geometrically
no. of
cubes
proportion
of surface
atoms
1.5 X 10 13
5 X 10 12
0.5 X 10 4
1.5 X 10 5
Area/ m 2
Dimensions of cube/nm
14-4
Surface area matters!
Exterior Surface and Particle Shape
Consider a cube 1m length each side
Surface area = 6 m2
If we break the cube into cubes
That are 0.1 m on each side we produce
1000 cubes.
Total surface Area = 60 m2 (1000 X 0.01 m2 )
If we cut the small cubes to have 1cm edges we get a million cubes
Surface area = 600 m2
Cubes with 1mm edges : 6000 m2
And so on
14-5
How many nanocubes each 1nm on edge can be carved from a parent cube 1m on edge?
What is the collective surface area of the nanocubes?
Solution:
Each edge would be composed of 109 edges of the nanocubes
So number of nanocubes = (109)3 = 10 27
Surface Area of each nanocube = 6 X (1 X 10-9) 2 m2
Surface area of all nanocubes = 6X10 27 X 10 -18 m2
= 6 X 10 9 m2 = 6000 km2
( a billion times that of the 1m cube)
As big as PEI
Area - Total: 5,683.91 km2 (2,195 SQ MI)
14-6
Shape
Surface Area depends on particle shape as well as size.
Common shapes of nanoparticles: cubes,spheres, cylinders,pyramids, discs
Tetrahedra, icosahedra, dodecahedrons, cubooctahedrons, tubes ……..
A cube with the same volume as a sphere has a higher surface area.
Discs and wires have highest surface areas
Sphere is lowest energy configuration of solid materials
Nanoparticles can assume shapes of the Bravais Lattices –see soon
14-7
Interior Nanoscale Surface Area
If a nanostructure is porous then it will have an additional internal surface area
IUPAC definitions:
Microporous: pore diam < 2nm
Mesoporous: pore diam 2 < 50
Macroporous pore diam > 50 nm
Most materials will have some form of porosity
and we have seen some methods
earlier to determine the pore structure sizes.
A porous solid is defined as one with
pores deeper than they are wide
microporous
Mesopores in anodized alumina
Zeolite MFI (ZSM-5)
14-8
SURFACE AND VOLUME
Recall general relationship between size-volume
In some nanomaterials all the atoms/ions
are surface.
proportion
of surface
atoms
Dimensions of cube/nm
14-9
Surface Atoms come into play under about 30 nm. This is important of course:
catalysis: more surface area: more active sites: faster reactions:
The power of small particles
The Lycurgus Cup: British Museum
a Roman goblet dating from the
fourth century A.D., changes
color when held up to the light.
The opaque green cup turns to a
glowing translucent red when
light is shone through it. The
glass contains tiny amounts of
colloidal gold and silver, which
give it these unusual optical
properties.
14-10
At what point does the number of surface atoms become significant?
Let's determine the number of surface atoms for a hypothetical piece of gold formed in
a simple cubic lattice. (Gold is actually a fcc metal)
see lecture 8-4 and again soon
14-11
Primitive Cubic Lattice
Calculate the number of Surface Atoms (Ns), edge atoms Ne, and Volume atoms Nv,
and the surface to volume atomic ratio Ns/Nv as size is decreased by a factor of 10,
starting with a 1 cm 3 block. Au radius 0.144 nm. AM =196.967, density D = 19.31g/cm3
Solution
First calculate the number of gold atoms per metre (cm,mm micrometer, nm etc)
Cube answer to get number of atoms. Take square X 6 to get Surface Area in terms
of number of atoms. Ns/Nv can then be calculated
14-12
'Brute Force" Method
Number of Au atoms in 1m = 1/0.288 X 10 -9 = 3.47 X 10 9
Volume = 4.19 X 1028 Gold atoms
Surface Area = 7.22 X 1019 Au atoms
Surface to Volume Ratio = 1.72 X 10 -9
14-13
ratio of surface atoms/total goes from one billionth to 88%
STRUCTURE
we are actually going to continue to learn about crystal structure
why? --because all nanomaterials seek the lowest energy (most stable)
form. These can be related to the known structures of larger crystals
Crystal Systems and the Unit Cell
Bravais lattice, named after Auguste Bravais is an infinite set
of points generated by a set of discrete translation
operations. A crystal is made up of one or more atoms (the
basis) which is repeated at each lattice point. The crystal then
looks the same when viewed from any of the lattice points. In
all, there are 14 possible Bravais lattices that fill threedimensional space.
14-14
Bravais Lattices
more next time......
14-15