1
Supplementary Information
Structural Diversity in Binary Nanoparticle Superlattices:
Beyond Hard Spheres.
Elena V. Shevchenko,1,2 Dmitri V. Talapin,1 Nicholas A. Kotov,3 Stephen
O’Brien2 and Christopher B. Murray1
1
IBM Research Division, T. J. Watson Research Center, 1101 Kitchawan Road,
Yorktown Heights, NY 10598, USA
2
Department of Applied Physics & Applied Mathematics, Columbia University, 200 SW
Mudd Building, 500 West 120th Street, New York, NY 10027, USA
3
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109,
USA
2
Supplementary Figure 1. (a) An overview TEM image of (100) projection of
AuCu-type superlattice self-assembled from 5.8 nm PbSe and 3.4 nm Ag
nanoparticles. (b) A magnified image of the same structure. (c) The modeled
(100) projection of AuCu-type binary superlattices (left) and the minimum
number of particle layers leading to the pattern identical to the observed one
(right). (d) A faceted “supercrystal” self-assembled from 6.2 nm PbSe and 5.0
nm Au nanoparticles and (e) its closer lookup.
3
Supplementary Figure 2. TEM images of different binary superlattices selfassembled from the same batches of 6.2 nm PbSe and 3.0 nm Pd
nanoparticles.
4
Supplementary Figure 3. (a-h) TEM micrographs of (001) planes of binary
superlattices isostructural with AlB2. Top left insets in (a), (b), (c), (e) and (f)
show the arrangement of NPs in AlB2-type superlattices at higher magnification.
Bottom right insets show small angle ED patterns measured along the (001)
projection. (i) – a unit cell of AlB2 lattice. (j) Depiction of the (001) plane. (k) Depiction of minimum number of nanoparticle layers along the (001) direction
necessary to reproduce the observed experimental patterns. The ratio of
particle radii (γ) for the reported AlB2-type binary superlattices varied from 0.43
to 0.79. The γ-range of stability for AlB2-type packing of hard spheres is 0.482
to 0.624 [11].
5
Supplementary Figure 4. Modeled projections of binary superlattices shown in
the Figure 1. The details of the structure modelling will be published elsewhere.
6
5
4x10
5
Intensity [a.u.]
3x10
5
2x10
5
1x10
0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-1 -1
mobility [mcmV s ]
Supplementary Figure 5. Distribution of the electrophoretic mobility for 4.8 nm
Au nanocrystals in chloroform. Similar behavior was observed for Ag
nanoparticles. The small size of Pd nanocrystals (~3 nm) did not allow us to
investigate their electrophoretic mobility with acceptable signal-to-noise ratio.
7
Discussion 1
Speculations on the processes by which Oleic acid and TOPO modify
nanoparticle charge.
Only a very slight modification of the ionic environment on the particle surface would
be required to generate nanoparticles with one or two non-compensated charges.
PbSe
The surface of as-prepared PbSe nanocrystals is, most probably, capped by oleate
(C17H33COO-) that covalently binds surface lead atoms and oleic acid (C17H33COOH)
that adsorbs at the nanocrystal surface. When an excess of oleic acid is introduced to the
solution there is the potential for protonation of some of the oleate species leaving
behind positively charged surface sites. Alternately, some oxidized selenium sites on the
PbSe nanocrystal surface could be protonated by the excess oleic acid increasing the
positive surface charge. These oxidized selenium surface sites form on exposure of the
PbSe nanocrystal colloids to air [J. S. Steckel, S. Coe-Sullivan, V. Bulović, M. B.
Bawendi Adv. Mater. 15, 1862 (2003).].
TOPO can form stable soluble-in-chloroform complexes with lead ions. Negative
charging of PbSe nanocrystals in the presence of TOPO might be due to dissolution of
positively charged lead ions from nanocrystal surface altering the particle stoichiometry.
Au
In the presence of oleic acid negatively charged oleate ions formed due to
autoprotonation of oleic acid molecules may associate with the particle surface. In
contrast, association of neutral TOPO molecules with the gold surface does not alter the
particle charge state.
8
Discussion 2
Electrostatic Binding Energy of a Binary Superlattice of Charged Nanoparticles
The Coulomb energy of an ionic crystal can be calculated by summing pair potential Vij
over all pairs of nanocrystals in the superlattice [M.P. Tosi, Solid State Physics:
Advances in Research and Applications, edited by F. Seitz and D. Turnbull, Academic
Press, New York, 1964 (Vol.16, pp.1-113)]:
U Coul
Zi Z je2
1
 
2 i j 40 Rij
(1)
If the positive and negative charges on nanocrystals exactly compensate each
other, the binding energy of the binary superlattice can be expressed through a
Madelung constant:
U Coul 
( N   N  )Z  Z  e 2
M
40 R0
(2)
where M is the Madelung constant for a lattice of N+ positively and N- negatively
charged nanoparticles with average charges of Z+ and Z-, respectively and R0 is the
nearest-neighbor distance. E.g., for a rock salt lattice M=-1.7476.
If the positive and negative charges on nanocrystals do not compensate each other
completely, i.e., the binary superlattice retains a certain residual net charge, the
Coulomb energy of a superlattice can be also calculated from (1). For example, for a
rocksalt lattice of N+ identical “cations” and N- identical “anions” the cohesive energy
of can be calculated as
U Coul 
Zj
Zj 
e2 
 NZ 
N  Z  

80 
j R j
j R j 

N
N
 N 1
 N 1
e 
1 
1 





N
Z
Z

Z

N
Z
Z

Z
   










80 
R
R
R
R
j
j
j
j

 

  



(3)
2
The expression (3) can be simplified because of the symmetry in the rocksalt
lattice:
U Coul  
N
NZ  Z  e 2
Ne 2
Z   Z  2  1
M
40 R0
80
j R 
(4)
9
The second term in the last expression contains the positive sum approx.
proportional to N2/3 because the number of like-charged neighbors increases as ~ R2 .
3D
U Coul


Ne 2
2
 2Z  Z  M   Z   Z   N 2 / 3
80 R0

(5)
with a pronounced minimum at Z+=-Z-, i.e., for an electrically neutral superlattice. The
value of β can be calculated numerically.
In a generalized case of an ABx superlattice, the Coulomb energy of a threedimensional superlattice consists of two terms:
3D
U Coul
  N   xZ  Z   N 5 / 3
2
(6)
Large domains of binary superlattices require precise charge compensation. For
a given   xZ  Z  ratio there is a critical size above which the Coulomb energy will
prevent further growth of the charge non-compensated binary superlattice.
Madelung constant per ion (M/υ where υ is the number of ions per “formula unit”)
is in range of 0.68 – 0.88 for the majority of binary lattices. The absolute values of
electrostatic cohesive energy are predicted to be similar, at least of the same order of
magnitude, for different binary lattices.