Particle Synthesis – Morphology Control
H.Hofmann
Powder Technology Laboratory
Institute of Materials
Swiss Federal Institute of Technology
Lausanne, Switzerland
http://ltp.epfl.ch
Prussian blue nanoparticle
Mann et al. Angew Chem Int 2000 39 1793
Assembly by epitaxial interaction
R. Lee Penn et al. J. Phys. Chem. B 2001, 105, 2177-2182
Formation of Oxalat particles by
2-D assembly of nanosized building blocks
2 min
5 min
8 min
12 min
Assembly of n-particles in 2-D
Growth of Cu-oxalate by agglomeration
Aspect ratio of Cu-Oxalate Crystals and Particles
Asp ect ratio o f Cu -O xalate p articles
8
7
6
5
4
3
2
0.7
1.2
1
1.7
2.2
0
3
0
0.5 49 nm
1
1.5
2
Aspect ratio of Cu-Oxalate crystals
Increasing HPMC concentration
0 g/L
0.625 g/L
2.5
3
3.5
Structure of the Particles
[110]
[001]
110
001
Cu
110
001
Oxalate
Cross section
Copper
Copper oxide
Structure of the particle
Dissolution in
under-saturated solution
Co-Oxalate-dihydrate
Surface step Growth mechanism
Core-Shell structure
Core
Shell
Particle synthesis by assembly
Calcium carbonate
1) Precipitation
of nano-particles and Growth of the seeds
2) Growth by Assembly
0.6 µm
PhD thesis Marcel Donnet, LTP-EPFL, 2002
0.6 µm
500 nm
S. Mann and H. Cölfen Angew. Chem. Int. Ed. 2003, 42, 2350 – 2365
Particle interaction
(Calculation for SiO2)
⎛ 1 ⎞ 1 −κ⋅rij
Fij =4π ⋅ε ⋅a ψ e ⎜ +κ⎟ e erij
⎜r ⎟r
⎝ ij ⎠ ij
2 2 2κa
R.Vacassy, R.J.Flatt, H.Hofmann; K.S.Choi and
R.K.Singh,
J.Colloid and Interface Sci. 227 (2000) 302-315
Agglomeration kinetic
(Smoluchowski)
Random Structured Core
Evolution of the size distribution in time, for gold colloid particles, average
particle radius as a function of time.
Simulation of aggregation (spherical particles):
The main assumption in the secondary particle growth has been that they
irreversibly capture primary particles, and at the same time restructure to
maintain compact, bulk-density, polycrystalline morphology..
S. Libert et al. / Advances in Colloid and Interface Science 100 –102 (2003) 169–183
Precipitation/Assembly
c/c0
104
Nucleation
Random, low density
growth
[N1]
N1c ??
1
Ordered
High density
aggregation
t
t
Thermodynamic of the Agglomeration Process
∆G = ∆H –T ∆S
∆H: γ(ΣSagglo – ΣScrystal)
1
b= αa
2
α aspect ratio of the primary crystal
α’ aspect ratio of the agglomerate
a
γ= surface energy of the primary crystal
γ’= surface energy of the agglomerate (γ = γ’)
γ’’= grain boundary energy
∆H
∆H == 2Nγa
2Nγa22[aα/a’α’
[aα/a’α’ {(a’/a)-1)αα’)+0,5((α’a’/αa)-1
{(a’/a)-1)αα’)+0,5((α’a’/αa)-1 ++ 2α’α+1}
2α’α+1} –(2α
–(2α22+1)]
+1)]
∆S
lnX ox+N
(V ox/V
∆S == -k{N
-k{NwwlnX
lnXww +N
+Nox
+Nox
/Vww)}
)}
oxlnXox
ox(Vox
Assembling of nanosized particles (relaxation)
Fast agglomeration
No or slow relaxation
*
time
Slow agglomeration
anisotropic properties of the crystal
relaxation possible
* Deng et al, J.Colloid and Interface Science 173 (1995) 79-85
Deposition of nanosized particles on surfaces
or large particles
Model: Random Sequential Adsorption (RSA)
X
Max. coverage ρmax without relaxation (2-D model):
ρ (circles) : 0.55
ρ(squares) : 0.562
Multilayer deposition and rearrangement?
V. Privmann, Colloids and Surfaces A, 165 (2000) 231 - 240
Thermodynamic of the Agglomeration Process
Free Entergy of Agglomeration
Surface energy: 0.1 J/m2
1,3 g Ox/l 293 K
0
-1
0
1000
2000
3000
4000
5000
Aspect ratio 1.2
Free Energy (J/l)
-2
Aspect
Ratio
(Crystals)
Particle
Size
µm
-4
1.2
0.95
-5
1.7
0,73
2.2
0.54
3
0.43
-3
Aspect ratio 1.7
Aspect ratio 2.2
Aspect ratio 3
-6
-7
Particle Size (nm)
Needs “Thermodynamic of small systems”, T. Hill 1964
Acknowledgement
P. Bowen
C. Soares
O. Puijul
F. Juillerat
M. Donnet
N.Jongen
NF
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