Energetic and entropic contributions to self-assembly of binary nanocrystal superlattices: Temperature as the structure-directing factor

Article abstract of DOI:10.1021/ja103083q

We studied the effect of temperature on self-assembly of monodisperse colloidal nanocrystals into single-component and binary superlattices. Temperature, which serves as a weighting factor for the internal energy (U) and entropy (S) contributions to the Helmholtz free energy F = U - TS, allows tailoring relative weights of the interparticle interactions and free-volume entropy during the formation of nanocrystal superlattices. Temperature also provides a convenient tool for directing self-assembly of nanocrystals toward desired superlattice structures. We found that temperature strongly affects the structures of binary superlattices self-assembled from the mixtures of CdSe + PbS nanocrystals and PbSe + Pd nanocrystals. In the former case, small Hamaker constants for CdSe and PbS nanocrystals led to a relatively simple phase diagram, including only high-density NaZn₁₃-, AlB₂-, and NaCl-type binary superlattices. In contrast, binary superlattices self-assembled at different temperatures from PbSe and Pd nanocrystals showed a number of low-density complex phases stabilized by strong local van der Waals interactions between Pd nanocrystals. The structural diversity of nanoparticle superlattices is shown to be a result of the cooperative effect of the entropy-driven crystallization and the interparticle interactions. Both ΔU and TΔS terms associated with the superlattice formation should be of the same order of magnitude, with |ΔU| < |TΔS| for the assembly of CdSe and PbS nanocrystals and |ΔU| > |TΔS| for the PbSe and Pd nanocrystals.

Full text of DOI:10.1021/ja103083q

Published on Web 08/11/2010
Energetic and Entropic Contributions to Self-Assembly of
Binary Nanocrystal Superlattices: Temperature as the
Structure-Directing Factor
Maryna I. Bodnarchuk,†,§ Maksym V. Kovalenko,† Wolfgang Heiss,‡ and
Dmitri V. Talapin*,†
Department of Chemistry and James Franck Institute, UniVersity of Chicago, Chicago, Illinois 60637,
and Institute of Semiconductor and Solid State Physics, Johannes Kepler UniVersity Linz,
A-4040 Linz, Austria
Received April 12, 2010; E-mail: dvtalapin@uchicago.edu
Abstract: We studied the effect of temperature on self-assembly of monodisperse colloidal nanocrystals
into single-component and binary superlattices. Temperature, which serves as a weighting factor for the
internal energy (U) and entropy (S) contributions to the Helmholtz free energy F ) U - TS, allows tailoring
relative weights of the interparticle interactions and free-volume entropy during the formation of nanocrystal
superlattices. Temperature also provides a convenient tool for directing self-assembly of nanocrystals toward
desired superlattice structures. We found that temperature strongly affects the structures of binary
superlattices self-assembled from the mixtures of CdSe + PbS nanocrystals and PbSe + Pd nanocrystals.
In the former case, small Hamaker constants for CdSe and PbS nanocrystals led to a relatively simple
phase diagram, including only high-density NaZn13-, AlB2-, and NaCl-type binary superlattices. In contrast,
binary superlattices self-assembled at different temperatures from PbSe and Pd nanocrystals showed a
number of low-density complex phases stabilized by strong local van der Waals interactions between Pd
nanocrystals. The structural diversity of nanoparticle superlattices is shown to be a result of the cooperative
effect of the entropy-driven crystallization and the interparticle interactions. Both ∆U and T∆S terms
associated with the superlattice formation should be of the same order of magnitude, with |∆U| < |T∆S| for
the assembly of CdSe and PbS nanocrystals and |∆U| > |T∆S| for the PbSe and Pd nanocrystals.
1. Introduction
colloidal solutions. It is anticipated that the rationally
engineered NC assemblies will provide novel opportunities
for electronic,14,15 optoelectronic,16 thermoelectric,17 cata-
lytic, and other applications. Progress in the development of
practical materials from NCs will require controllable growth
of SLs with desired structures and morphologies and should
rely on a deep understanding of the physics and chemistry
of NC self-assembly.
One of the most fascinating directions in contemporary
materials research is the use of precisely engineered mol-
ecules and nanostructures as the building blocks for hierar-
chical self-assembly of functional materials and devices.1-4
Among such materials, the long-range ordered arrays of
colloidal nanocrystals (NCs) attract steadily growing funda-
mental and practical interest. Owing to excellent size and
shape uniformity, NCs can spontaneously order into single-
component superlattices (SLs)5-7 and binary nanocrystal
superlattices (BNSLs)1,8-13 upon evaporation of concentrated
The formation of single-component NC SLs is rather well
understood5,18-20 and can be controllably achieved for different
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Kim, Y. M.; Kim, Y. J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 3023–
3027.
† University of Chicago.
‡ Johannes Kepler University Linz.
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§ On leave from Johannes Kepler University Linz.
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J. AM. CHEM. SOC. 2010, 132, 11967–11977 11967

A R T I C L E S
Bodnarchuk et al.
materials. At the same time, previous studies have demonstrated
that co-assembly of two types of NCs can yield BNSLs
exhibiting very rich phase diagrams with multiple close-packed
and non-close-packed periodic10,21 and even aperiodic quasic-
rystalline phases.22 Recently, Vanmaekelbergh’s group has
reported self-assembly of ternary nanoparticle superlattices.23
At the same time, little is known about the driving forces for
BNSL formation. So far, most experimental studies used highly
empirical and serendipitous choices of experimental conditions
for BNSL growth and did not provide a thorough assessment
of thermodynamic and kinetic factors contributing to the NC
assembly process.
From a thermodynamics perspective, the problem of finding
the equilibrium configuration for a large ensemble of particles
can be treated as minimization of the Helmholtz free energy
(F).24,25 For a closed system F is generally expressed through
the internal energy (U), entropy (S), and temperature (T):
To apply existing theoretical framework to real NCs, we need
quantitative estimates for all terms contributing to U and S in
eq 1. Unfortunately, there is no current agreement on the
hierarchy of the energy scales acting during self-assembly of
NCs into BNSLs. Enormous structural diversity and observation
of non-close-packed BNSL phases suggest the important role
of specific pair potentials.10 Simple estimations predict that the
strengths of Coulombic, dipolar, and vdW forces between
individual NCs should be of the same order of magnitude,46
further complicating theoretical analysis of BNSL phase dia-
grams. On the other hand, Chen and O’Brien recently studied
self-assembly of CdSe and CdTe NCs and proposed that the
formation of BNSL from these NCs was mainly driven by free
volume entropy, leading to the structures with the highest
packing density for a given particle size ratio.9 Their observa-
tions of CdTe-CdTe BNSLs isostructural with AlB2, NaZn13,
CaCu5, and MgZn2 intermetallic compounds have been rational-
ized on the basis of simple space-filling principles, long known
for colloidal hard spheres.5,33
F ) U - TS
(1)
In this work we report an experimental study of the effect of
temperature on the formation of single-component and binary
NC superlattices. According to eq 1, temperature can be used
as the weighting factor for the energetic and entropic contribu-
tions. The role of entropy can be effectively increased by
increasing the temperature while keeping all other parameters
constant, thus offering a tool for predictable screening of BNSL
phase diagrams and for guiding the NC self-assembly toward
desired structures.
The contributions to the free energy of the equilibrium
ensemble can be subdivided into energetic and entropic. The
internal energy is determined by specific interactions between
NCs, which can interact with each other in a very complex
manner, just like atoms in metallic,26 ionic, or molecular
crystals.27,28 Experimental studies of various NC systems have
revealed Coulombic,10,29 dipole-dipole,30 and van der Waals
(vdW)31 interactions between NC inorganic cores. Furthemore,
the hydrocarbon tails of the NC ligand molecules can interact
with each other, generating either attractive or repulsive forces,
depending on solvent and interparticle distance.32 The entropy
changes during the self-assembly process are generally related
to the vibrational and configurational degrees of freedom,5,33
as will be discussed below.
2. Experimental Section
2.1. Nanocrystal Synthesis. PbSe NCs stabilized with oleic acid
were synthesized from lead oleate and TOPSe. The details of
preparation can be found in ref 14. Synthesis of PbS NCs capped
with oleic acid was performed from lead oleate and bis(trimethyl-
silyl)sulfide according to ref 47. CdSe NCs were synthesized
according to ref 48 from dimethylcadmium and TOPSe in a mixture
of hexadecylamine, trioctylphosphine oxide, and trioctylphosphine.
The synthesis of FexO/CoFe2O4 core-shell NCs was carried out
by high-temperature decomposition of mixed iron(III)/cobalt(II)
oleate at 320 °C in the presence of oleic acid as the stabilizing
agent.49 Dodecanethiol-stabilized 3.4 and 4.9 nm Pd NCs were
synthesized as described in ref 10. Palladium acetate was used
instead of palladium chloride as precursor for synthesis of 4.9 nm
Pd NCs, and the reaction was carried out at 60 °C.
Thermodynamics of sphere packing is an active research field,
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11968 J. AM. CHEM. SOC. VOL. 132, NO. 34, 2010

Self-Assembly of Binary Nanocrystal Superlattices
A R T I C L E S
In many cases, the comparison of experimental TEM images
with two-dimensional (2D) projections of modeled crystal structures
was sufficient for unambiguous structural assignments of BNSL
structures. In several cases, however, this approach could lead to
erroneous conclusions because of similarities in the BNSL projec-
tions of different structures. For example, the (100) projection of
the AlB2-type lattice (Figure S1a) appears similar to the (010)
projection of the CuAu lattice (Figure S1b). To obtain information
about three-dimensional (3D) packing of NCs in BNSLs, we
complemented real-space TEM studies with the SAED patterns
measured from BNSL domains. Compared to real-space images,
SAED contains information about the 3D arrangement of NCs in
the unit cell. Thus, similar real-space images shown in Figure S1a,b
correspond to distinctly different electron diffraction patterns (Figure
S1e,f) with different interplanar spacings (1/dhkl). The ratios between
different dhkl values are uniquely defined by the lattice symmetry.
On the basis of these ratios, we assigned the experimental electron
diffraction in PbSe-Pd superlattices to the CuAu-type structure
(Figure S1g). In some cases, Fourier transformation of TEM images
can also provide useful information (Figure S1h,i).
In TEM tilting experiments, BNSL structures can be viewed at
different angles with respect to the electron beam. This technique
provides the most direct information about 3D arrangements of NCs
in the unit cell.54,55 We applied this technique to distinguish between
(100) projections of AlB2 structure and (010) projections of CuAu-
type BNSLs (Figure S2). TEM tilting experiments were also
employed to distinguish between (001) projections of CuAu and
(001) projections of CsCl-type BNSLs (Figure S3) and to study a
complex structure formed from 7.7 nm PbSe and 3.4 nm Pd NCs
(Figure S4).
Figure 1. Setup used for studies of self-assembly of different nanocrystals
into single-component and binary superlattices at various temperatures.
2.2. Preparation of Binary Superlattices at Different Tem-
peratures. We used an experimental setup shown in Figure 1 to
carry out self-assembly experiments in the temperature range
between -60 and 120 °C. Carbon-coated copper TEM grids (type-
B, Ted Pella) were used as the substrates for self-assembly
experiments. The grids were dipped in toluene for 15 s to remove
protective Formvar coating, followed by drying on filter paper. The
grids were placed inside a tilted glass vial (∼60° tilt angle).
Approximately 20 µL of solution containing a mixture of two types
of NCs with the desired particle ratio was placed above the grid to
cover it entirely. Concentrations of NCs were estimated either
photometrically for CdSe, PbS, and PbSe using known extinction
coefficients50-52 or gravimetrically for all other NCs. In the latter
case, the concentrations were corrected for ligand fraction known
from thermogravimetric analysis of purified NC samples. Additional
details are provided in the Supporting Information.53 Various
n-alkanes (octane, nonane, decane, undecane, dodecane, tetradecane,
hexadecane, and octadecane) were used as solvents. The vials were
placed in a cooling bath containing an organic solvent/dry ice
mixture to obtain temperatures from -60 to -20 °C, in water/ice
for 0 °C, or in an oil bath to reach 20-140 °C. The following
cooling mixtures were used: tetrachloroethylene/dry ice for -20
°C, acetonitrile/dry ice for -40 °C, and isopropyl ether/dry ice for
-60 °C. The solutions were evaporated under dynamic vacuum
supplied via a needle penetrating the cap of the closed vial. The
evaporation rate could be easily adjusted by using different gauge
needles.
To maximize the reproducibility of self-assembly experiments,
we carried out all temperature-dependent studies using the same
batches of NCs for the entire temperature range. Each experiment
was reproduced at least twice to ensure reproducibility of reported
trends.
2.3. Structural Characterization of Nanocrystal Superlat-
tices. Transmission electron microscopy (TEM) images and electron
diffraction patterns were obtained using an FEI Technai F3
microscope operating at an acceleration voltage of 300 kV. The
TEM images were compared to the BNSL projections simulated
using Accelrys MS Modeling 4 and Crystal Maker 1.4 software
packages. Small-angle electron diffraction (SAED) patterns mea-
sured over large BNSL areas were compared with the FFTs of real-
space TEM images and with electron diffraction patterns simulated
with Single Crystal 1.2.1 software.
2.4. Measurements of Electrophoretic Mobility of Colloidal
Nanocrystals. Measurements of electrophoretic mobility were
performed using Zetasizer Nano-ZS (Malvern Instruments, Inc.).
Colloidal solutions were tested using a dip-cell setup with Pd
electrodes. Typical measurements of electrophoretic mobility
included several scans of 100 runs each in the high-resolution mode.
Dilution was optimized for each sample to achieve >100 kcps count
rate and the best signal-to-noise ratio. The voltage applied to
colloidal solutions was typically between 10 and 20 V.
3. Results and Discussion
3.1. Self-Assembly of Single-Component Nanoparticle Su-
perlattices at Different Temperatures. Since we could not find
any previous systematic studies related to the effect of temper-
ature on self-assembly of NCs, we first studied how temperature
affects the assembly of monodisperse NCs into single-
component SLs. We used 11 nm FexO/CoFe2O4 NCs,49 which
exhibited a strong tendency to self-assemble into superlattices56
at different temperatures. Chloroform was used as a solvent
providing good solubility for FexO/CoFe2O4 NCs and suitable
for the temperature range from -60 to +45 °C.
Both entropy and isotropic vdW interactions should favor the
structures with highest packing density, namely face-centered
cubic (fcc) and hexagonal close-packed (hcp).57 In a hard-sphere
system, fcc is favored over hcp due to its higher entropy,
although the free energy difference is very small, about 10-3kBT
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(53) For more details see Supporting information.
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A R T I C L E S
Bodnarchuk et al.
In addition to isotropic vdW forces between inorganic cores
and organic ligands, magnetic NCs exhibit anisotropic dipolar
magnetic interactions. As was previously reported,49 FexO/
CoFe2O4 NCs possess rather small saturated magnetization of
15 emu/g (7.8 × 104 A/m), as compared to 90-100 emu/g (4.7
× 105-5.2 × 105 A/m) for bulk CoFe2O465 and 70-100 emu/g
(3.7 × 105-5.2 × 105 A/m) for CoFe2O4 NCs of similar
size.66-68 This was attributed to the presence of an antiferro-
magnetic FexO core and some disorder of surface spins. The
role of magnetic interactions between NCs becomes progres-
sively more important with lowering the temperature of the self-
assembly process. The blocking temperature (TB) measured by
SQUID magnetometry for 11 nm NCs was 160 K, i.e., well
below -40 °C (233 K) used in our self-assembly experiments.
At the same time, TB strongly depends on the experimental time
scale. The mean time between two spin flips, also known as
the Ne´el relaxation time (τN), is given by
τN ) τ0 exp(KV/kBT)
(2)
where τ0 is the attempt time, typically 10-9 s,69 K is the
magnetic anisotropy, and V is the NC volume. The time scale
of SQUID measurement (τN ) 100 s) is very different from
the time scales for adding of NCs to a growing superlattice.
Recent in situ GISAXS studies70 allow estimating that the
appropriate time scale should lie in the millisecond domain.
Without further speculations, we can obtain from eq 2 that,
at this time scale, 11 nm FexO/CoFe2O4 NCs with SQUID-
measured TB ) 160 K should interact as ferromagnets up to
temperatures as high as 290 K. The magnetic interaction
energy (UM) between two ferromagnetic NCs can be calcu-
lated as UM ) (1/9)πµ0R3M2 ≈ 3 × 10-3 eV,39 where µ0 is
the permeability of free space, R is the NC radius, and M is
the magnetization. This value approaches ∼0.15kBT at -40
°C and is more than an order of magnitude larger than the
interaction energy between fluctuating dipoles of two super-
paramagnetic NCs, known as the Kreesom interaction,39
estimated as ∼10-5 eV. In a SL the magnetic dipoles of
individual NCs are additionally stabilized by local dipole-
dipole interactions.71 On longer time scales the magnetization
of a NC should switch between three mutually orthogonal
(001)-type easy axes of CoFe2O4 phase. The local coupling
of magnetic dipoles combined with dynamic switching of
magnetization of individual NCs between several easy axes
could be responsible for stabilization of the ncp structure
shown in Figure 2d.
Figure 2. TEM images of superlattices self-assembled from chloroform
solutions of 11 nm FexO/CoFe2O4 nanocrystals at different temperatures:
(a) face-centered cubic structure was formed at 45 °C; (b) face-centered
cubic and hexagonal close-packed structures were formed at 25 °C; (c)
hexagonal-close-packed structures were dominant at -20 °C; and (d) non-
close-packed structures were formed at -40 °C.
per particle.58 In addition, the solvent flow can direct NCs
toward the fcc lattice.59 In our case, the fcc structure formed
almost exclusively at +45 °C (Figure 2a). When self-assembly
of NCs was carried out at 25 °C, we observed the coexistence
of hcp and fcc lattices (Figure 2b). Fcc and hcp structures could
be easily distinguished in TEM images and electron diffraction
patterns (Figure S5). At -20 °C the hcp structure became
dominant (Figure 2c), with minor inclusions of non-close-packed
(ncp) structures. The ncp hexagonal ordering was reproducibly
observed in NC superlattices self-assembled at -40 °C (Figures
2d, S6, and S7).
The ncp structure shown in Figures 2d, S6, and S7 can be
described as a stack of staggered hexagonally ordered layers
rotated by an angle R with respect to each other. We modeled
possible superlattice projections (Figures S6b) and found that
the pattern with R ) 30° is identical to that of the ncp structure
self-assembled from 11 nm FexO/CoFe2O4 NCs at -40 °C.
Similar SLs have been previously reported for Au NCs.60,61 To
explain the formation of such low-density packing, Schiffrin et
al. suggested that strong short-range electrostatic repulsion
forced the NCs to occupy two-fold saddle points rather than
three-fold hollow points above the underlying monolayer.60
Similar structures with mutually rotated, hexagonally ordered
2D sheets have been observed for atomic layers in MoS2,62 for
block-copolymer thin films,63 and in DNA crystals.64
Theoretical studies of dipolar spheres have revealed that the
energy of dipolar coupling (Madelung energy) for the hcp lattice
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11970 J. AM. CHEM. SOC. VOL. 132, NO. 34, 2010

Self-Assembly of Binary Nanocrystal Superlattices
A R T I C L E S
is higher than that for the fcc lattice.72 The Madelung energy is
proportional to m2, where m is the particle magnetic moment.
Upon increasing the strength of dipolar forces, phase transitions
from fcc to hcp to base-centered orthorhombic and tetragonal
(bco, bct) phases have been reported theoretically42,73 and
experimentally74 in ensembles of spherical particles. The fcc
structure should be more stable at high temperatures, while hcp
should dominate at low temperatures. This is because the
advantage that the hcp lattice gains from U in eq 1 is canceled
at high T by the entropic term -TS.
Figure 2 shows that temperature can be a structure-directing
factor in self-assembly of magnetic NCs. We also performed
similar studies with nonmagnetic NCs (Au, Pd) and found a
strong preference for the formation of fcc superlattices at all
studied temperatures, as expected for crystallization of spherical
particles with isotropic interparticle potentials.
(ε′ - 1)/(ε′ + 2) ) 4πdNAR/3Mw
(3)
where ε′ is the real part of the dielectric constant, d is the density,
R is the polarizability of molecule, and Mw is the molecular
weight. For n-alkanes, ln(1/d) ) a/Mw - b, where ln a )
0.00275T + 2.303 and b ) 0.000182T1.19 80 One can easily show
.
that the ε′ values for the above-described sequence of n-alkanes
chosen as solvents for BNSL self-assembly lie in the narrow
range of 1.99-2.04 due to the compensation of the higher
dielectric constant for longer chain alkanes by the temperature
effect on ε′. Available experimental data on ε′ of n-alkanes fully
confirm this trend.81 Through similar “compensation” between
Mw and thermal energy, the viscosity of the studied NC solutions
remained nearly independent of temperature as well.82 Chemical
inertness is another important advantage of using n-alkanes as
solvents.
In our experiments it took about 20-25 min to completely
evaporate 25-30 µL of colloidal solution under mild vacuum.
To maintain reproducible solvent vapor pressure inside the vials,
we used the same gauge needles (Figure 1). In a series of
reference experiments, we varied the needle gauge to tune the
evaporation rate. The common result was that the type(s) of
BNSL structure(s) and their approximate fractions remained
independent of solvent evaporation rate. This led us to the
conclusion that the assembly process occurs mostly under
thermodynamic control.
3.2. Interparticle Interactions and Design of Experiments
for Growing BNSLs. To date, all reported experiments on BNSL
growth were carried out at 40-70 °C.1,9,10,13,15,75-78 There are
no obvious reasons for this choice other than NC solubility21
and experimental convenience. Toluene or tetrachloroethylene
was routinely used at these temperatures under ambient or
reduced pressure. In the case of magnetic FexO/CoFe2O4 NCs,
we used chloroform as a solvent convenient for low tempera-
tures. This approach, however, cannot provide acceptable
accuracy for NCs interacting via electrostatic forces because of
the strong temperature dependence of the static dielectric
constants of common organic solvents. The other problem
associated with using the same solvent for self-assembly of NCs
at different temperatures is related to different solvent evapora-
tion rates at different temperatures. We found no individual
solvents suitable over a broad temperature range of -60 to 120
°C. At the same time, chemically different solvents can interact
differently with NC surface ligands and thus alter the interpar-
ticle potentials.79 To address all these problems, we carried out
BNSL assembly in n-alkanes. The use of n-alkanes allowed us
to vary the assembly temperature without significantly changing
the solvent evaporation rate and dielectric constant, while
providing similar chemical environments for a broad range of
temperatures. We used a suitable n-alkane for each temperature
point. For example, the equilibrium vapor pressures fall in the
range of 0.5-0.6 Torr for hexane at -60 °C, heptane at -40
°C, octane at -20 °C, nonane at 0 °C, dodecane at 20 °C,
tetradecane at 40 °C, hexadecane at 65 °C, and octadecane at
85-100 °C. The static dielectric constant (ε′) of n-alkanes obeys
the Clausius-Mossotti relation:80
The surface charge (Z in units of e) for a spherical particle
in a low dielectric solvent can be estimated on the basis of the
measured electrophoretic mobility:83
µe ) Ze/6πηR
(4)
where η is the solvent dynamic viscosity and R is the
hydrodynamic radius. The ε′ values of the n-alkanes used in
this work (1.99-2.04)80 were significantly lower than the ε′
values of chlorinated (4.8 for chloroform at 25 °C) or aromatic
(2.5 for toluene at 25 °C) solvents. Our electrophoretic mobility
measurements showed that NCs possess considerable surface
charge when dispersed in chloroform, whereas the low dielectric
constants of n-alkanes reduced the effects of NC surface
charging in nonpolar solvents.10 For example, the population
of charged 7.7 nm PbSe NCs in chloroform was significantly
larger than in n-decane (Figure S8a,b). The electrophoretic
mobility of 4.9 nm dodecanethiol-capped Pd NCs measured in
n-decane at different temperatures did not reveal any charging
of NCs. When corrected for temperature-dependent variations
of solvent viscosity, µe of Pd NCs was found to be temperature-
invariant (Figure S8c,d).
3.3. Remarks on Entropy and Packing Density. The packing
density plays an important role in intermetallic compounds,84
liquid crystals,24 opals,33,85 and NC superlattices.9 The total
entropy of an ideal gas of two types of particles (1:1 number
ratio) is86
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A R T I C L E S
Bodnarchuk et al.
5
2
N
V
S ) N - N ln
- 3N ln λ + ln 2
(5)
(
)
where V is the volume, λ is the thermal de Broglie wavelength,
and the term ln 2 accounts for the entropy of mixing. This
formalism can be qualitatively applied to a NC solution. In
general, S of an ordered array of spherical particles can be
subdivided into configurational entropy and free volume
entropy.34,36,37 As solvent evaporates, the concentration of NCs
increases and the free volume decreases. When the average
interparticle distance becomes comparable to the particle
dimensions, the system can undergo a transition from a
disordered to an ordered state. The ordering reduces configu-
rational entropy but leads to higher free volume entropy
associated with the local free space available for each particle
to perform translational and rotational movements. It has been
shown that the gain in free volume entropy upon ordering of
hard spheres can be larger than the decrease in configurational
entropy, thus providing a net positive change in the system’s
entropy. This purely entropic effect forces the phase transition
and stabilizes the ordered colloidal crystal state.34,58
Figure 3. Calculated space-filling curves for NaCl, CsCl, CuAu, AlB2,
MgZn2, Cu3Au, CaCu5, and NaZn13 binary structures. Dashed vertical lines
show γeff for nanocrystals studied in this work.
The free volume entropy is related to the packing density of
a SL. It is often asserted that the free volume per particle is
inversely related to the packing fraction of a crystalline structure
and that the entropy is proportional to the free volume.87 In the
absence of other significant forces, the ensemble of spheres
should adopt a structure with the highest packing density. In
the case of monodisperse particles, it will be fcc or hcp lattices
with F ≈ 0.7405, whereas in binary mixtures, the most favorable
structure should be one with the highest density for a given
particle size ratio γ ) dsmall/dlarge. Space-filling curves plotting
the space-filling factor (F) versus γ can be used to estimate
relative entropic contributions to the change in free energy
during the self-assembly process. Figure 3 shows calculated F
vs γ curves for BNSL structures observed in this study (see
Supporting Information for calculation details). Space-filling
provides a good estimate for entropic contributions. At the same
time, configurational entropy can help direct the assembly
process between structures with similar F values. Thus, the
slightly higher configurational entropy of the fcc lattice makes
it more stable than hcp;58 the higher configurational entropy of
the aperiodic lattice compared to the periodic one stabilizes
quasicrystalline NC superlattices.22
formation at different relative concentrations of NCs. γeff was
calculated using actual NC sizes estimated as dNC ) dcore
+
2dshell, where dshell was the effective thickness of the ligand shells.
Typically dshell is smaller than the length of fully extended ligand
molecules (e.g., 18 and 15.2 Å for oleic acid and 1-dode-
canethiol, respectively), suggesting interpenetration of hydro-
carbon tails of adjacent NCs.90 NC size, material, and even
sample preparation conditions can affect the packing density
of surface ligand molecules. For example, successive washing
of colloidal PbSe NCs partially removes oleic acid ligands
attached to the NC surface, making the ligand shell effectively
thinner. On the other hand, excessive washing often negatively
affects the ability of NCs to self-assemble. In this work we
measured dshell as half the mean interparticle distance for single-
component fcc SLs. This approach was used in previous
works75,91 and allows estimation of dshell relevant to NC
assembly. For NCs studied in this work, dshell values were 1.1
nm for CdSe NCs synthesized in TDPA-HDA-TOPO-TOP
mixture, 0.95 nm for oleic-acid-capped PbSe NCs, 0.85 nm for
oleic-acid-capped PbS NCs, 0.85 nm for 3.4-nm dodecanethiol-
capped Pd NCs, and 1.1 nm for 4.9-nm dodecanethiol-capped
Pd NCs.
We studied self-assembly in three different NC systems: (i)
8.0 nm CdSe and 3.1 nm PbS NCs (γeff ) 0.47 ( 0.02), (ii)
7.7 nm PbSe and 3.4 nm Pd NCs (γeff ) 0.53 ( 0.03), and (iii)
7.7 nm PbSe and 4.9 nm Pd NCs (γeff ) 0.74 ( 0.03). The
mean γeff values for the studied systems are shown in Figure 3
as vertical lines. The standard deviations for γeff were calculated
for each system from experimentally measured NC size
distributions. This choice of NCs was motivated by the
availability of convenient synthetic routes toward monodisperse
CdSe, PbSe, PbS, and Pd NCs. The Hamaker constants for
metals interacting through a hydrocarbon layer are significantly
larger than for metal chalcogenides,92 and the vdW interactions
between Pd NCs should be stronger than those between PbSe
NCs. This difference originates from different dielectric re-
sponses of metals and dielectrics at the differerent optical
When F of a binary lattice exceeds that of a fcc structure,
entropy alone can stabilize ABn structure against phase separa-
tion into separately packed A and B components.34 Accurate
free energy calculations also predict that binary phases of hard
spheres whose F is slightly below 0.7405 can be stabilized by
additional configurational entropy and the entropy of mixing
(eq 5).88 Binary structures with F < 0.7405 can also be stabilized
by interparticle interactions.89 The conformational changes of
surface ligands during formation of SLs should also provide an
entropic contribution to the free energy of NC self-assembly.
Little is known about the magnitude of this contribution.
3.4. Formation of BNSLs at Different Temperatures. In this
study we used several fixed size ratios of small and large NCs
(γeff ) dsmall/dlarge) and studied how temperature affects BNSL
(87) Hynninen, A. P.; Filion, L.; Dijkstra, M. J. Chem. Phys. 2009, 131,
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Shevchenko, E. V. J. Am. Chem. Soc. 2009, 131, 16386–16388.
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Chem. Soc. 2007, 129, 15702–15709.
(88) Xu, H.; Baus, M. J. Phys. Condens. Matter 1992, 4, L663–L668.
(89) Leunissen, M. E.; Christova, C. G.; Hynninen, A.-P.; Royall, C. P.;
Campbell, A. I.; Imhof, A.; Dijkstra, M.; van Roij, R.; van Blaaderen,
A. Nature 2005, 437, 235–240.
(92) Bergstro¨m, L. AdV. Colloid Interface Sci. 1997, 70, 125–169.
9
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Self-Assembly of Binary Nanocrystal Superlattices
A R T I C L E S
Figure 4. Self-assembly of 8 nm CdSe and 3.1 nm PbS nanocrystals at different temperatures. (a) Overview of the binary phases assembled at different
temperatures. (b-d) Typical electron microscopy images of binary superlatices isostructural with (b) NaZn13, (c) AlB2, and (d) NaCl compounds.
frequencies.93 Comparative studies of CdSe-PbS and PbSe-Pd
NC systems allow the situations to be studied where the
components have similar Hamaker constants, as in the former
case, or show a large contrast in the strength of vdW forces, as
in the latter case. Compared to Au and Ag, palladium NCs
showed much better solubility in n-alkanes at low temperature,
presumably because of denser coverage of the NC surface with
dodecanethiol ligands. The choice of effective γ-ratios studied
in this work was also justified by the availability of calculated
phase diagrams for hard spheres at γ ) 0.45,37 0.52 and 0.54,94
and 0.72 and 0.74,87,94 which allowed comparison of the
behaviors of real NCs with the entropy-driven crystallization
of hard spheres.
The only binary structure self-assembled at 85 °C from the
mixtures of CdSe and PbS NCs was isostructural with NaCl
(Figure 4a,d). At 65 °C, NaCl-type was the dominant binary
structure, but we also observed the formation of small domains
of AlB2-type BNSLs, representing ∼10-20% of all formed
BNSL structures (Figure 4a,c). When the same NCs were mixed
with the same concentrations but solvent was evaporated at 0,
25, or 40 °C, we reproducibly observed formation of AlB2-
type BNSLs. These two structures are the densest phases and
have nearly identical packing densities of about 0.729 at γ )
0.47 (Figure 3). Further decrease of temperature led to the
formation of NaZn13-type lattice (Figure 4a,b) with much smaller
calculated packing density (∼0.658). The BNSLs shown in
Figure 4 were all obtained from the solutions with ∼1:8
concentration ratio for CdSe and PbS NCs. To adjust for the
differences in NBSL stoichiometry, the NaCl- and AlB2-type
BNSLs coexisted on TEM grids with domains of fcc-packed
PbS NCs. The samples with NaZn13-type BNSLs also contained
CdSe NCs in the form of either disordered or fcc-packed
domains.
density of the fcc lattice, and should be strongly favored by the
free volume entropy. Rather surprisingly, the most common
BNSL structures self-assembled from colloidal solutions of 7.7
nm PbSe NCs and 3.4 nm Pd NCs (γeff ≈ 0.53) were not AlB2-
type but CuAu- and Cu3Au-type BNSLs with packing fractions
of only F ≈ 0.60 (Figure 5a-c). Figure 5a shows BNSL phases
assembled at different temperatures from solutions with 1:9
PbSe-to-Pd NC concentration ratio. Formation of CuAu and
Cu3Au structures was observed at -20, 40, 85, and 100 °C. At
low temperature (-20 °C) these BNSLs co-existed with NaZn13
(∼20% of all formed BNSL domains) and AlB2-type BNSLs
(∼35%). Near room temperature, the high-density AlB2 phase
(Figure 5f) dominated at all studied PbSe-to-Pd NC ratios. At
65 and 85 °C we observed reproducible formation of another
binary phase (Figure 5h), resembling the Fe4C lattice.10 This
structure was studied using TEM tilting experiments (Figure
S4) and assigned to a BNSL with AB4 stoichiometry, containing
32 small spheres and 8 large spheres per unit cell (Supporting
Information). At 100 °C only CuAu and Cu3Au BNSLs were
observed. Table S1 in the Supporting Information compares the
areas of TEM grids covered by different BNSL structures at
each temperature.
When the concentration of Pd NCs was increased to ∼1:18
PbSe-to-Pd NCs ratio, we observed a similar sequence of BNSL
phases self-assembled at different temperatures (Figure 5b). The
major difference compared to the 1:9 concentration ratio was
the increased probability to form NaZn13-type structures, which
were the only BNSLs formed at -20 °C. NaZn13 BNSLs were
also observed at 25 °C (∼20%) co-existing with AlB2 and other
BNSLs. At high temperatures we observed only CuAu- and
Cu3Au-type BNSL phases (Figure 5b). When the PbSe-to-Pd
NC concentration ratio was lowered to ∼1:4.5, no NaZn13-type
BNSLs were observed. Instead, we observed the formation of
NaCl-type BNSLs at low temperatures (Figure 5c). At inter-
mediate and high temperatures, the NCs self-assembled into
AlB2-type and CuAu + Cu3Au BNSLs, respectively. TEM
images of different PbSe-Pd BNSL phases are shown in Figure
5d-i. Additional TEM images of BNSLs assembled at different
temperatures are provided in the Supporting Information
(Figures S9-S12).53
To explore a binary system of typical semiconductor and
metal NCs, we studied co-assembly of PbSe and Pd NCs for
two different particle size ratios (γeff ) 0.53 and 0.74) at
different temperatures and for different NC concentration ratios.
Figure 3 shows that, at γ ) 0.53, AlB2 structure has its highest
packing density (F ≈ 0.782), significantly exceeding the packing
(93) Visser, J. AdV. Colloid Interface Sci. 1972, 3, 331–363.
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A R T I C L E S
Bodnarchuk et al.
Figure 5. Effect of temperature on self-assembly of 7.7 nm PbSe and 3.4 nm Pd nanocrystals. (a-c) Overview of binary phases self-assembled at different
temperatures from solutions with nanocrystal concentration ratios of (a) 1:9, (b) 1:18, and (c) 1:4.5. (d-i) TEM images of BNSLs isotructural with (d) NaCl,
(e) CuAu, (f) AlB2, (g) Cu3Au, (h) AB4,53 and (i) NaZn13 intermetallic compound.
Simultaneous formation of several BNSL phases could be
either due to the existence of several binary phases with very
similar chemical potentials or due to inhomogeneities in the
NC samples. In addition to unavoidable size dispersion, some
NCs can have small electric charge while other can be neutral.10
Similar distribution can exist in the NC dipole moments. It is
difficult to separate these effects, but the observation that,
depending on the temperature, identical NC mixtures can form
either only one BNSL structure or several BNSL structures (e.g.,
Figure 5a-c) suggests degeneration of BNSL structures at
certain temperatures.
Figures 6d-i and S13 show typical TEM images of all BNSL
structures self-assembled from 7.7 nm PbSe and 4.9 nm Pd NCs.
3.5. Analysis of the Effect of Temperature on BNSL Self-
Assembly. Figures 4-6 show that different colloidal NCs self-
assemble at different temperatures into distinctively different
BNSL phases. The reproducible formation of different binary
phases from identical NC solutions can be used as a powerful
synthetic tool for directing the self-assembly process. It also
provides important insight into the thermodynamics of the NC
assembly process.
As discussed in section 3.2, proper selection of solvents can
provide nearly temperature-independent electrostatic and vdW
forces between NC cores. The interactions between hydrocarbon
chains of surface ligands can be temperature-dependent, as was
shown by atomistic molecular dynamics simulations by Vlugt
et al.32 At the same time, in a good solvent like n-alkane, direct
ligand-ligand interactions are efficiently screened and become
purely repulsive, providing steric stabilization to NC colloids.32
This picture changes dramatically after solvent evaporation,
which converts ligand-ligand interactions from repulsive to
strongly attractive.32,95
To compare the self-assembly of BNSL structures from NCs
with the same chemical compositions but different γeff ratios,
we synthesized 4.9 nm Pd NCs and studied their co-assembly
with 7.7 nm PbSe NCs (γeff ≈ 0.74). For the highest Pd-to-
PbSe NC concentration ratios, we again observed the formation
of NaZn13 BNSLs at low temperatures (Figure 6a,d), despite
its rather low packing density (F ≈ 0.61 at γ ) 0.74). This
structure disappeared for lower Pd-to-PbSe NC ratios, being
replaced by the CaCu5-type BNSL (Figure 6b,c,h). The space-
filling curve for the CaCu5 lattice has a high-density branch
with F ≈ 0.67 at γ ) 0.74 (Figure 3), which can explain the
appearance of this structure at large γ. Also, contrary to the
system with γ ) 0.53, we observed MgZn2-type Laves-phase
BNSLs self-assembled at 65 °C. The packing density of the
MgZn2 lattice is much higher at γ ) 0.74 than at γ ) 0.53
(Figure 3). The CuAu and CsCl structures showed a clear
domination at higher temperatures (Figure 6, Table S2), which
is also consistent with their highest packing density for this γ.
Each BNSL structure has characteristic internal energy and
entropy {UAB ;SAB } per particle. The relative weights of internal
n
n
energy and entropy scale according to eq 1. With increasing
temperature, the role of SAB increases, and BNSLs with larger
n
entropic components should become more stable compared to
the structures stabilized by interparticle interactions. Since the
(95) Mueggenburg, K. E.; Lin, X.-M.; Goldsmith, R. H.; Jaeger, H. M.
Nat. Mater. 2007, 6, 656–660.
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Self-Assembly of Binary Nanocrystal Superlattices
A R T I C L E S
Figure 6. Self-assembly of 7.7 nm PbSe and 4.9 nm Pd nanocrystals at different temperatures. (a-c) Schematic illustration of binary phases assembled at
different temperatures from solutions with different nanocrystal concentration ratios. (d-h) TEM images of BNSLs isostructural with (d) NaZn13, (e) CuAu,
(f) MgZn2, (g) AlB2, (h) CaCu5, and (i) CsCl structures.
free volume entropy is approximately proportional to F, it is
reasonable to expect that high-temperature phases should also
have the highest packing density for a given γ ratio.
basis of increasing the colloidal stability of NC solutions up to
the concentrations required for the AlB2fNaCl phase transition
(transitions IV and V in eq 6).
In an 8 nm CdSe-3.1 nm PbS NC system (γeff ≈ 0.47), the
temperature-driven transition from the low-density NaZn13-type
BNSLs to the high-density AlB2 and NaCl structures (Figure
4) follows this expected trend. We could not find calculated
phase diagrams for hard-sphere mixtures at γ ) 0.47, but the
calculations by Trizac et al. for the close case of γ ) 0.45 predict
that both NaCl and AlB2 binary structures can form from hard
spheres at this γ.36 The mixture of hard spheres with the
concentration ratio of large to small spheres nL:nS ) 1:8 should
undergo the following sequence of phase transitions upon
gradual increase of the particle concentration:36
Eldridge et al. calculated the range of stability for NaZn13
structures in hard-sphere mixtures as 0.474 e γ e 0.626.25 γeff
of our CdSe-PbS NCs is very close to the lower boundary of
this stability range, and formation of NaZn13-type BNSLs is
not totally unexpected. Moreover, the finite size distributions
of CdSe and PbS NCs can create sub-ensembles of NCs with
γeff values sufficient to entropically stabilize the NaZn13 lattice.
These arguments, however, cannot explain why we did not
observe any other BNSL structures at low temperature and did
not observe NaZn13 BNSLs at higher temperatures. The most
plausible explanation is that the cohesive energy of NaZn13
BNSLs is higher compared to those of AlB2 and NaCl BNSLs
and of close-packed PbS NCs. The internal energy term then
rivals free volume entropy at low temperatures but is not
sufficient to dominate over the -T∆S term at high temperatures.
The possible reasons for energetic stabilization of NaZn13
BNSLs will be discussed later.
Self-assembly of PbSe and Pd NCs (Figures 5 and 6) resulted
in a significantly richer palette of binary phases compared to
the CdSe-PbS system. We attribute this to strong vdW interac-
tions between Pd NCs, which increased the total weight and
complexity of energetic contributions to the free energy of self-
assembly. BNSLs self-assembled from mixtures of 7.7 nm PbSe
and 3.4 nm Pd NCs (γeff ≈ 0.53) included both the binary phases
expected for hard spheres (NaZn13, AlB2, NaCl) and a number
of low-density phases, such as CuAu, Cu3Au, and the AB4 lattice
shown in Figure S4. The phase diagrams calculated for binary
I
II
III
IV
F ⇒ (AlB2 + F) ⇒ (AlB2 + S + F) ⇒ (AlB2 + S) ⇒
V
(AlB2 + NaCl + S) ⇒ (NaCl + S) (6)
where F and S stand for the fluid (disordered phase) and the
fcc lattice of small particles, respectively. The AlB2 phase should
form first during solvent evaporation. In a hard-sphere system
this binary phase converts to the NaCl-type lattice when the
particle volume fraction exceeds ∼0.65. In real NCs, the
presence of attractive vdW forces can destabilize NC solutions
before approaching this volume fraction and “freeze” the NCs
in the AlB2 phase, which probably occurs at 0-40 °C. It is
known that the solubility of NCs capped with hydrocarbon
surface ligands increases with temperature. We may then explain
the formation of the NaCl phase at high temperatures on the
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A R T I C L E S
Bodnarchuk et al.
hard-sphere mixtures at γ ) 0.54 predicted formation of AlB2
and NaZn13 binary phases,94 which was verified in the experi-
mental studies by Hunt et al. on sterically stabilized PMMA
spheres with γ ) 0.52.94 The behavior of PbSe and Pd NCs
revealed stark disagreement with both theory and the experi-
ments on PMMA spheres. Instead of two binary phases
assembled from PMMA spheres, the NCs formed at least six
binary phases. At low temperatures (-20 to 25 °C) we observed
NaZn13 BNSLs when Pd NCs were present in a large excess
compared to PbSe NCs (Figure 5a,b,i). At low PbSe-to-Pd NC
ratios, NaCl-type was the sole low-temperature BNSL phase
(Figure 5c,d). At high temperatures CuAu and Cu3Au were the
dominant BNSL phases (Figure 5e,g). These structures have F
≈ 0.60 at γ ) 0.53, which is much lower than the density of
AlB2 packing. Our study clearly showed that co-assembly of
7.7 nm PbSe and 3.4 nm Pd NCs cannot be explained by
entropy-driven crystallization. Instead, self-assembly of these
NCs should be primarily driven by interparticle interactions.
To further explore the driving forces responsible for self-
assembly of PbSe and Pd NCs, we combined 7.7 nm PbSe with
4.9 nm Pd NCs (γeff ≈ 0.74). In hard-sphere calculations, this
γ ratio is known to form no thermodynamically stable binary
phases,87,94 which was also confirmed in experimental studies
on PMMA particles.94 In contrast to these predictions, PbSe
and Pd NCs formed six different BNSL phases (Figure 6d-i).
The low-density NaZn13 (F ≈ 0.61) BNSL was the low-
temperature phase. The CuAu and CsCl BNSLs were assembled
at high temperatures, which is also in agreement with their
highest F values among all BNSLs self-assembled from 7.7 nm
PbSe with 4.9 nm Pd NCs. Comparison of BNSL phases formed
between PbSe and Pd NCs at different γ shows that the space-
filling principles are not totally ignored in these BNSLs. For
example, CaCu5 structure was observed at γ ) 0.74 and not
observed at γ ) 0.53, in agreement with its higher packing
density at large γ (F ≈ 0.67 vs 0.59 for the above γ ratios,
respectively). The same applies to the MnZn2 BNSL, with F
approaching reasonably high values only at large γ ratios (Figure
3).
Figure 7. Unit cells of binary nanoparticle superlattices self-assembled at
different temperatures. See text for discussion of BNSL structural evolution
caused by energetic and entropic contributions to the free energy of self-
assembly.
anticipated in recent theoretical studies96 and requires a delicate
competition between attractive potentials and kBT.
Another interesting trend observed in all three NC systems
is schematically outlined in Figure 7. The low-temperature
BNSL phases (NaZn13 and CaCu5) comprised a sub-lattice of
large NCs separated by clusters of small NCs. In the NaZn13
lattice these clusters include 13 NCs. The clustering in the CaCu5
lattice is less evident, but the structure can be deconvoluted
into a simple hexagonal packing of large spheres and close-
packed trigonal bipyramidal clusters of five small spheres. The
AlB2 lattice typically observed at intermediate temperatures
contains “clusters” of two small NCs (Figure 7). All high-
temperature BNSL structures (NaCl, CuAu, CsCl, and Cu3Au)
have no touching small spheres. If small NCs exhibit stronger
attractive forces than large NCs, the binary lattices incorporating
“clusters” of small NCs should gain additional stability from
short-range attraction between tightly packed small NCs. This
should be especially evident in the PbSe-Pd system because of
strong vdW interactions between Pd NCs.
Formation of many BNSL phases in a relatively small
temperature window requires that |∆U| and |∆TS| in eq 1 should
be of the same order of magnitude, with |∆U| < |∆TS| during
assembly of CdSe-PbS NCs and |∆U| > |∆TS| for PbSe-Pd NCs.
The driving force of NC self-assembly gradually shifts from
the interparticle interactions (low-T limit) to free-volume entropy
(high-T limit), leading to NaZn13 BNSLs at low temperatures,
whereas the high-temperature structures should be those with
the largest F for each γ ratio.
The observed difference in the self-assembly behavior of
CdSe-PbS and PbSe-Pd NCs outlines the general complexity
principle in BNSL structures. Since the Hamaker constants for
both CdSe and PbS phases interacting through a layer of
hydrocarbon ligands are comparable, the vdW contribution to
the free energy should scale approximately with the lattice packing
density, and simple hard-sphere packing models should reasonably
accurately describe behaviors of real NCs. On the other hand, if
there is a large difference in interaction energies between large
and small NCs (e.g., in BNSLs combining semiconductor and metal
NCs), BNSL phase diagrams gain complexity, leading to non-
compact phases and even truly complex binary structures such as
Archimedean tailings and quasicrystals.22
An important general observation which can be derived from
our experimental data is that, in all three studied systems, NaZn13
BNSLs formed exclusively at low temperatures. We can propose
two possible explanations for such behavior. First, the assembly
of AB13-type lattice can be largely driven by the ∆U in eq 1
rather than by the free volume entropy. The second possibility
is related to the kinetics of NC assembly. The assembly pathway
for NaZn13 lattices could involve pre-assembly of icosahedral
clusters of Pd NCs in solution driven by vdW and electrostatic
forces, followed by the integration of these clusters into growing
NaZn13 lattices (Figure S14). Such cluster assembly has been
4. Conclusions
We have shown that temperature can be used as a convenient
tool for directing self-assembly of NCs into different single-
component and binary structures. A comparison of calculated
hard-sphere phase diagrams with our experimental studies of
(96) Keys, A. S.; Glotzer, S. C. Phys. ReV. Lett. 2007, 99, 235503.
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11976 J. AM. CHEM. SOC. VOL. 132, NO. 34, 2010

Self-Assembly of Binary Nanocrystal Superlattices
A R T I C L E S
DMR-0213745 and by the David and Lucile Packard Foundation.
M. I. B. and W. H. acknowledge financial support from the Austrian
Nanoinitiative (NSI). The work at the Center for Nanoscale
Materials (ANL) was supported by the U.S Department of Energy
under Contract No. DE-AC02-06CH11357.
NC assembly revealed significantly richer behavior of NCs
compared to the non-interacting spherical particles. In the
absence of strong electrostatic interactions and vdW forces, as,
e.g., in the CdSe+PbS BNSLs, hard-sphere phase diagrams
correlated well with the behaviors of real NCs at high temper-
atures. On the other hand, self-assembly of BNSLs including
metal NCs (e.g., PbSe+Pd) cannot be rationalized using hard-
sphere models because of strong interparticle interactions.
Contrary to the case of CdSe-PbS NCs, entropy seems to play
only a limited role in the stabilization of PbSe-Pd BNSLs. The
observed structural diversity of BNSLs is a result of comparable
contributions of entropy-driven crystallization and interparticle
interactions, with the possibility of adjusting energetic and
entopic contributions through chemical design of NCs and with
many complex binary phases formed under appropriate experi-
mental conditions.
Supporting Information Available: Additional experimental
and calculation details; structural characterization of BNSLs
using electron diffraction (Figure S1) and TEM tilting studies
(Figures S2-S4); TEM images for close-packed and non-close-
packed superlattices of FexO/CoFe2O4 NCs (Figures S5-S7);
electrophoretic mobility measurements for colloidal NCs used
in self-assembly experiments (Figure S8); calculation details
for space-filling curves; additional TEM images of BNSLs self-
assembled from PbSe and Pd NCs (Figures S9-S13); summary
of surface area coverage by different binary superlattice
structures (Tables S1 and S2); pathway for self-assembly of
BNSL structures with complex unit cells incorporating clusters
of metal NCs (Figure S14). This material is available free of
charge via the Internet at http://pubs.acs.org.
Acknowledgment. We thank E. V. Shevchenko (Argonne
National Laboratory), A. Moore and T. Witten (University of
Chicago) for stimulating discussions, and S. M. Rupich (University
of Chicago) for synthesis of PbS and PbSe nanocrystals. The work
was supported by the NSF MRSEC Program under Award No.
JA103083Q
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