Polycatenar Ligand Control of the Synthesis and Self-Assembly of Colloidal Nanocrystals

Article abstract of DOI:10.1021/jacs.6b04979

Hydrophobic colloidal nanocrystals are typically synthesized and manipulated with commercially available ligands, and surface functionalization is therefore typically limited to a small number of molecules. Here, we report the use of polycatenar ligands d

Full text of DOI:10.1021/jacs.6b04979

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Article
Polycatenar Ligand Control of the Synthesis
and Self-Assembly of Colloidal Nanocrystals
Benjamin T. Diroll, Davit Jishkariani, Matteo Cargnello, Christopher B. Murray, and Bertrand Donnio
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Polycatenar Ligand Control of the Synthesis and Self-
Assembly of Colloidal Nanocrystals
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Benjamin T. Diroll,1†‡ Davit Jishkariani,1,2‡ Matteo Cargnello,1# Christopher B. Murray1,3* and Ber-
trand Donnio2,4*
1Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, United States.
2Complex Assemblies of Soft Matter Laboratory (COMPASS), UMI 3254, CNRS-Solvay-University of Pennsylvania,
Bristol, PA 19007, United States
3Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, United
States
4Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), UMR 7504, CNRS−Université de Strasbourg,
67034 cedex 2, Strasbourg, France
KEYWORDS. Ligands, Nanocrystal Synthesis, Self-Assembly, Hard Sphere, Polycatenar
ABSTRACT: Hydrophobic colloidal nanocrystals are typically synthesized and manipulated with commercially available
ligands and surface functionalization is therefore typically limited to a small number of molecules. Here, we report the
use of polycatenar ligands derived from polyalkylbenzoates for the direct synthesis of metallic, chalcogenide, pnictide,
and oxide nanocrystals. Polycatenar molecules, branched structures bearing diverging chains in which the terminal sub-
stitution pattern, functionality, and binding group can be independently modified, offer a modular platform for the de-
velopment of ligands with targeted properties. These ligands are used not only for the direct synthesis of monodisperse
nanocrystals, but nanocrystals coated with polycatenar ligands self-assemble into more softer bcc superlattices that devi-
ate from conventional harder close-packed structures (fcc or hcp) formed by the same nanocrystals coated with commer-
cial ligands. Self-assembly experiments demonstrate that the molecular structure of polycatenar ligands encodes interpar-
ticle spacings and attractions, engineering self-assembly which is tunable from hard sphere to soft sphere behavior.
Introduction
influence the self-assembly behavior of NC-ligand hybrids
including thermally-5,33 or photo-switchable structures.34
Colloidal NCs coated with various types of mesomor-
phous ligands have demonstrated self-assembly into
many liquid crystalline and crystalline assemblies.5–7,28–36
Most efforts rely on post-synthetic ligand-exchange, alt-
hough direct syntheses of colloidal NCs have been report-
ed with Au NCs near room temperature.35–37 In these ex-
amples the size distribution of NCs is large, indicating
that the tight control over the NC size has until now not
been achieved in direct synthesis with non-commercial
ligands.
Research on the ligands bound to colloidal nanocrystals
(NCs) is maturing into the significance that has long been
achieved in other fields of chemistry. Ligand coatings can
be used to control solubility,1–4 self-assembly,5–8 thermal
stability,9,10 optical properties,11 electronic conduction,12
catalysis,13 magnetism,14 medical therapies,15 and NC syn-
thesis.16 With some important exceptions, the toolset of
available ligands is limited to commercial sources, leaving
space for synthetic design of tailored ligands. Indicating
the potential of ligand design, DNA-coated NCs in aque-
ous media demonstrate ligand-controlled self-assembly
and sensing.17–19 Similarly, precise matching of inorganic
metal chalcogenide ligands with CdSe NCs yields films of
exceptional conductivity.20
Here, we demonstrate the direct synthesis of monodis-
perse NCs using polycatenar ligands. These ligands14 are
composed of an anchoring group to bind the particle
surface, a branched tail of alkyl chains to enhance solubil-
ity, and a triazole ring linking the two components to-
gether. Our modular synthetic strategy accesses polycate-
nar ligands with independently-tunable peripheral chain
substitution and functionality and diverse anchoring
groups to bind NCs of different chemical compositions.
To demonstrate their wide utility, we use these ligands to
For NCs in hydrophobic media, ligands are typically
paraffinic alkyl amines, phosphines, thiols, carboxylic or
phosphonic acids. These remain invaluable, but the fields
of liquid crystals and supramolecular chemistry show the
structural complexities and practical utility achievable
through thoughtful exploitation of organic chemistry.
Recent efforts have demonstrated coating of colloidal NCs
with dendritic or liquid-crystalline ligands5–7,14,21–32 that
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synthesize a broad range of nanocrystals including cad- ble to similar syntheses using commercial reagents. Self-
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mium and lead chalcogenides, ZnO, Fe2O3, InP, and Au.
assembly into single-component and binary nanocrystal
superlattices (BNSLs) demonstrate the excellent mono-
dispersity of NCs prepared by direct synthesis with poly-
catenar ligands. The longer organic ligand shells strongly
affect self-assembly, as NC behavior becomes softer, di-
verging further from the organizing principles of hard
spheres. In single-component systems, polycatenar lig-
ands induce a size-dependent transition from close-
packed hard structures (fcc or hcp) to softer bcc superlat-
tices. The BNSL phases which are observed in these softer
NC superlattices largely conform to the predicted trends
of recent theoretical work on the phase diagram for bina-
ry colloidal NCs with soft interaction potentials.38
Direct synthesis, as opposed to ligand-exchange, has
both advantages and limitations: it is more demanding of
material stability, but enables ligand-dependent control
of the resulting NCs and their properties with unambigu-
ous surface termination. In ligand-exchange reactions,
sterically-hindered ligands are particularly problematic
candidates to bind to particle surfaces and the ligand
shells may be incompletely exchanged. Nonetheless, lig-
and molecules may function non-innocently in reactions,
so we also perform ligand exchange with polycatenar
ligands on selected NCs.
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For optimized reactions, direct synthesis with poly-
catenar ligands yields NCs with monodispersity compara-
Scheme 1. Synthesis of the various libraries of polycatenar ligands arranged according to their functionalities.
Reagents and conditions: (i) Hydrazine, THF, 60 ͦC, 4h; (ii) Thiourea, EtOH, reflux, 12h. The complete characterization of ligands
20a-q as well as the synthesis of the precursors 5a-e,9,10,16 and all other intermediates 1a-c through 8 are described in details in
Supporting Information.
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we relied upon the Huisgen “click” cylcloaddition chemis-
Experimental Section
try.40 To study the influence of the triazole ring orienta-
tion and the presence of benzylic methylene unit we also
prepared corresponding phenyl acetylene 10 as model
system (making 20i).39 This late-stage functionalization
permits independent variation of the ligand structure—
e.g. number and length of chains and anchoring function-
ality—which enables a study of the influence of such
parameters on NC properties and allows broader compat-
ibility with NCs of diverse chemistries.
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Full details of materials, synthetic procedures, and
characterization methods are contained in the Supporting
Information file.
Results and Discussion
Ligand Synthesis and Design. Ligands used in the di-
rect synthesis of NCs must survive the thermal and chem-
ical conditions of reactions in addition to stabilizing NCs
against aggregation. Building from the known stability of
alkyl and phenyl ethers in NC synthesis, the peripheral
functionalization of the polycatenar ligands is achieved
via Williamson ether synthesis (Scheme 1).39 Thermal
analysis indicates the success of this approach: decompo-
sition of the ligand material occurs at >300 °C, similar to
oleic acid. (See Supporting Information Figure S1) The five
libraries of ligands in Scheme 1 are synthesized in a
modular approach. For one half, peripheral units of lipo-
philic alkyl-decorated polyhydroxbenzoates are function-
alized as azides (5a-e, 9). For the other component, sur-
face-anchoring groups with carboxylic or phosphonic
acid, amine, and thiol binding groups are terminated with
alkynes (11-19). To synthesize the final targets (20a-20q),
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The ligands 20a-q fall into five libraries that address
changes of ligand design. Library 1 consists of ligands 20a-
d with different anchoring spacer lengths but identical
(C12) alkyl substitution pattern, and library 2 (20e-f) con-
sists of longer (C18) homologs. Ligands with different
number and substitution pattern of alkyl end groups 20g-
j together with an example of a ligand with differently
oriented triazole unit 20i are shown in library 3. Library 4
consists of ligands where we introduce aromatic rings
either at the periphery (as end groups) 20k or the anchor-
ing unit 20l. Non-carboxylate ligands (20n, 20p-q) are
gathered in library 5.
Figure 1. (a) Optical absorption spectra, (b) X-ray diffraction patterns, and (c) TEM micrographs of NCs prepared by direct syn-
thesis with polycatenar ligands. CdS, InP, Fe2O3, PbS, and PbSe samples are capped with ligand 20b. The CdTe sample is capped
with ligand 20q, CdSe with 20d, ZnO with 20i, and Au with 20n.
Synthesis of Nanocrystals. The results of several syn-
theses of different NCs are shown in Figure 1. Reaction
conditions are typically chosen with little adjustment
from literature practice, replacing commercial fatty acid,
amine, or phosphonic acid ligands with equimolar
amounts of polycatenar analogs (Full details in Support-
ing Information). Figure 1a shows the UV to near-IR ab-
sorption spectra and Figure 1b shows the X-ray diffraction
patterns for examples of each material. The optical spec-
tra are similar to reported work, indicating formation of
the desired NC compositions. For the semiconductor NCs
which exhibit quantum confinement, first absorption
features reflect inhomogeneous broadening of electronic
structure, primarily due to size dispersion: the first ab-
sorption features of CdS, CdSe, CdTe, PbS, and PbSe NCs
are comparable to previous reports of monodisperse sem-
iconductor NCs.41–43 X-ray crystal structures observed in
direct synthesis with polycatenar ligands are consistent
with stable polymorphs for each of the materials. Au NCs
show an fcc structure, ZnO NCs exhibit the wurtzite crys-
tal structure whereas CdS, CdSe, CdTe, and InP exhibit
zinc blende crystal structures and lead chalcogenides
form in the rock-salt structure. The X-ray structures of
maghemite (Fe2O3) and magnetite (Fe3O4) are not suffi-
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ciently different for phase assignment in this case. The sized with polycatenar ligands show excellent monodis-
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assignment to the fully-oxidized maghemite phase is
made on the basis of past literature, which has shown that
small crystallites are easily oxidized into maghemite.44
persity apparent from the absorption spectra in Figure 2.
Under the same reaction conditions, the size of the result-
ing CdSe NCs varied from 2.4 to 6.0 nm according to the
ligand that was used. As the ligand size increased, the
resulting size of the NCs generally increased, although the
relation is imperfect. This suggests that larger ligands
suppress nucleation leading to fewer nuclei and larger
NCs. Consistent with this view, the largest ligand 20e
yields large (>50 nm) prismatic NCs (see Supporting In-
formation Figure S19). Not all ligands shown in Scheme 1
produced monodisperse CdSe NCs when used in pilot
reactions. Reactions with ligands 20h and 20j, with dis-
tinct peripheral chain substitution, produce soluble CdSe
NCs with an average size consistent with the trend of
steric hindrance (reactions with 3,5-branched 20h pro-
duced smaller NCs than with 3,4-branched 20j) but insuf-
ficiently monodisperse to demonstrate long-range self-
assembly. Monoalkyl (20g), triphenyl (20k), and benzo-
ate-anchoring (20l) derivatives showed poor solubility in
situ and resulted in polydisperse, frequently aggregated
products. In particular, the distinction between branched
and unbranched structures in NC solubility provides ad-
ditional support for enhanced solubility of NCs incorpo-
rating ligands with branches.45 When ligand-exchange is
performed on oleate-capped CdSe NCs, those exchanged
with 20k, containing phenyl peripheral functionality,
become insoluble in hexane but remain soluble in tolu-
ene; those exchanged with the 20g and 20l are insoluble
in nonpolar organic solvents such as hexanes, toluene,
and chloroform. These experiments highlight the signifi-
cant role of the ligand structure motifs in preserving sol-
ubility of the colloids during reactions.
TEM micrographs confirming the formation of NCs ap-
pear in Figure 1c. TEM confirms the low polydispersity
apparent from optical absorption spectra for many sam-
ples. The standard deviation of diameters for the cadmi-
um and lead chalcogenides was < 10% of the average di-
ameter in all cases, unless noted. Synthetic conditions for
InP (2.6 nm ± 0.5 nm) and Fe2O3 (4.4 nm ± 0.9 nm) NCs
in particular likely require further optimization; however,
ZnO samples (7.0 nm ± 0.8 nm) with polycatenar ligands
were sufficiently monodisperse to self-assemble into hcp
superlattices. Although the ZnO inorganic cores are more
polydisperse than typically required for self-assembly, the
organic coating counteracts inhomogeneity of the inor-
ganic component and fosters ordered assembly.
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Thermal analysis, FT-IR, and NMR experiments con-
firm that intact polycatenar ligands coat the surface of
NCs. Thermogravimentric analysis experiments confirm
the increase in organic weight fraction for 20b-capped 2.8
nm CdSe (45 wt%) compared with oleate-capped 2.8 nm
CdSe NCs (34 wt%). FT-IR experiments show the absence
of olefinic C-H bonds (Supporting Information Figure S6)
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in polycatenar-capped NCs and H NMR of 2.4 nm 20d-
capped CdSe or 20a-capped 7.0 ZnO, cleaned by precipi-
tation five times to remove excess ligand, unambiguously
shows NMR signals associated with the functional groups
of 20d or 20a, respectively (Supporting Information Fig-
ures S7 and S8).
Single-Component NC Self-Assembly. Nanocrystals
prepared by direct synthesis or coated through ligand-
exchange with polycatenar ligands showed size- and lig-
and-dependent self-assembly. To obtain self-assembled
structures from hard spheres typically requires ≤5% di-
ameter inhomogeneity and therefore self-assembly is a
powerful demonstration of monodispersity. By softening
differences of inorganic size, polycatenar ligands facilitate
self-assembly into periodic single-component superlattic-
es and BNSLs even in those cases (e.g. ZnO) where the
nanocrystals would seem too polydisperse. Figure 3 shows
typical self-assembly behavior of NCs with polycatenar
ligands (more in Supporting Information). Figure 3a
shows the (110) projection a bcc superlattice of 20b-
capped 2.8 nm CdSe and Figure 3b shows the same pro-
jection for a superlattice of 20b-capped 2.4 nm CdS nano-
crystals. Larger NCs prepared by direct synthesis includ-
ing (Figure 3c) 20i-capped 7.0 nm ZnO and (Figure 3d)
20b-capped 5.5 nm PbSe NCs self-assembled into hexag-
onally-packed superlattices.
Figure 2. Visible absorption spectra of CdSe NCs synthesized
with different polycatenar carboxylic acids as the ligands.
The chemical structure of the ligand used in each synthesis is
shown at right in the same color.
CdSe was used as a pilot system to study the effect of
different ligands on NC synthesis. NCs of CdSe synthe-
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different size. Figures 4a and 4b show 2.8 nm CdSe NCs
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capped with ligand 20a, which formed bcc assemblies, or
oleic acid, which formed close-packed superlattices. TEM
studies of CdSe samples showed that the effective solid
state ligand length (defined as one half of edge-to-edge
distance) of polycatenar ligands used in this work varied
from 1.4 nm (20d) to 2.2 nm (20a) as compared with ~1
nm for oleic acid. The larger spacings engineered with
polycatenar ligands are critical for generating deviation
from hard sphere behavior. Using a ligand with two
branches rather than three hardens self-assembly behav-
ior: Figures 4c and 4d show polymorphism in 20i-capped
3.5 nm CdSe NC superlattices, for which the ligand shell
thickness is ~1.8-1.9 nm. This suggests a turning point in
the self-assembly behavior where the contribution of the
organic material eclipses the contribution of the inorganic
material to the total diameter of the organic-inorganic NC
unit. A further demonstration is shown in by 20p-capped
6.5 nm and 3.0 nm Au NCs. The observed ligand layer
thickness of 20p-capped gold was larger than 20b-capped
semiconductors, presumably due to the larger number of
binding sites and consequently greater ligand density.
With a ligand of fixed length of 2.2 nm, 6.5 nm Au NCs
show hcp and fcc superlattices (Figure 4e) and 3.0 nm Au
NCs show bcc superlattices (Figure 4f). This strongly sug-
gests that the large relative organic size of softer systems
increasingly stabilizes the more open bcc structure. In-
deed, bcc superlattices were observed exclusively from
NCs with organic thickness greater than the particle radi-
us, with all NCs larger than ~4 nm showing hexagonal-
packing.
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Figure 3. (001) projection of (a) bcc 20b-capped 2.8 nm ± 0.2
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nm CdSe and (b) 20b-capped 2.4 nm ± 0.2 nm CdS, (c) (001)
projection of hcp 20i-capped 7.0 nm ± 0.8 nm ZnO, and (d)
close-packed hexagonal monolayer of 20b-capped 5.5 nm ±
0.4 nm PbSe NCs.
The observation of bcc superlattices, rather than a sta-
ble hard sphere phase, raises several lines of inquiry. In
the remainder of Figure 4, we separately examine the
influence of the ligands on the same size of NC, the effect
of branching, and the use of the same ligands on NCs of
Figure 4. (a) bcc-type self-assembly of 2.8 ± 0.2 nm CdSe NCs prepared by direct synthesis with ligand 20a. (b) hcp-type assem-
bly of 2.8 nm ± 0.2 nm CdSe NCs prepared by synthesis with oleic acid ligands. (c, d) 3.5 nm CdSe NCs capped with 20i poly-
catenar ligand self-assembled into hcp, fcc, and bcc superlattices. (e) hcp superlattice of 20p-capped 6.5 ± 0.4 nm nm Au NCs.
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Inset shows an fcc assembly of the same sample. (f) 20p-capped 3.0 nm ± 0.4 nm Au NCs in a bcc superlattice. The inset shows
another region of bcc superlattices for the sample, including a characteristic twin boundary.
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Previous work has claimed that bcc structures are ob-
served for small (<3 nm) NCs with oleate ligands as the
bcc structure reduces ligand frustration due to a highly-
symmetrical truncated octahedron shape of the Voronoi
polyhedron.46 NCs may also deviate from hard sphere
behavior because they are not spheres: 7.5 nm oleate-
capped PbSe nanocrystals form bcc structures, such as in
Supporting Information Figure S26, but this represents
the highest packing density structure for such truncated
octahedra. In the case presented in this work, the ob-
served behavior is dependent on the organic ligand
choice, as the inorganic cores (e.g. in Figures 4a and 4b)
are nearly identical in size, shape, and monodispersity,
but the size of the organic layer is substantially different.
(See comparison of SAXS and SANS in Supporting Infor-
mation Figure S23)
where ꢉ is the center-to-center distance of j and h NCs, r
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9
ꢁꢂ
is interparticle distance, ꢇ is a scalar reflecting the
strength of interaction. For potentials p≤7, the bcc phase
also becomes stable.47 Softness, judged from the size of
organic shell relative to the inorganic core determined by
TEM measurements,48 maps intuitively onto different
values of p. Samples in which the organic material is
smaller than the inorganic core size, like 20p-capped 6.5
nm Au NCs or oleate-capped 2.8 nm CdSe NCs, behavior
is “hard” (p>7), with the formation of hcp or fcc superlat-
tices. For systems with organic coatings that are larger
than the NC radius, including all NCs with diameters <4
nm with three-branch polycatenar ligands, exclusively bcc
superlattices are observed. With two-chain 20i-capped
CdSe, polymorphism between bcc, fcc, and hcp phases is
observed, suggesting similar energies of all three phases
(p≈7). From self-assembly data, we conclude that engi-
neering polycatenar ligands enables softer interparticle
potentials (p≤7) than previous NC systems with commer-
cial ligands.48
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A separate treatment of soft sphere behavior, which al-
so offers a unified approach with BNSLs, is based on in-
terparticle potentials of the form38,47
ꢋ
ꢉ
ꢃ ꢅ
ꢀ
ꢁꢂ
ꢄ ꢆ ꢇ ꢈ ꢁꢂꢊ
ꢄ
Figure 5. TEM micrographs of (a) NaZn13, (b) Cu3Au, and (c) CuAu BNSLs composed of different stoichiometries of 20b-capped
5.5nm PbSe and 20d-capped 2.4 nm CdSe NCs capped with polycatenar ligands. (d) CaCu5 BNSL composed of 20i-capped 3.5 nm
CdSe and 20i-capped 7.0 nm ZnO NCs. (e) MgZn2 and (f) CaCu5 BNSLs composed different stoichiometries of 20i-capped 3.5 nm
CdSe and 20b-capped 2.4 nm CdS NCs. The colorized inset of (f) shows 12-fold symmetric defects which occur in mixtures of the
two NCs. (g) Cu3Au-type, (h) CuAu-type, and (i) AlB2-type BNSLs formed from different stoichiometries of oleate-capped 2.8 nm
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CdSe and 20p-capped 6.5 nm Au NCs. Insets of (g) and (h) show images from other BNSL domains of the same type. Cartoons of
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the unit cell for each crystal structure are inset at the bottom left of the images.
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Table 1.Tabulated particle sizes and distances of NCs forming BNSL structures.
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a
b
d
Large NCs
oleate-CdSe
20p-Au
Small NCs
20d-CdSe
20d-CdSe
oleate-CdSe
20d-CdSe
20b-CdS
dlarge
5.3
dsmall
2.4
2.4
2.8
2.4
2.4
3.5
tlarge
1.0
tsmall
1.4
γc
SAB
BNSL(s)
MgZn2
0.71
1.40
0.64
0.45
0.70
1.05
1.00
1.00
0.91
6.5
6.5
5.5
3.5
2.2
2.2
2.0
1.9
1.4
0.48
0.44
0.55
0.88
0.68
0.89
0.90
CuAu,Cu3Au
CuAu, AlB2, Cu3Aue
NaZn13, Cu3Au, AlB2, CuAu
CaCu5, MgZn2
CaCu5
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20p-Au
1.0
20b-PbSe
20i-CdSe
20i-ZnO
20b-PbSe
20p-Au
1.4
2.0
1.9
20i-CdSe
20b-CdSe
20b-CdSe
7.0
3.5
1.9
2.7
2.0
2.2
2.0
2.0
MgZn2
6.0
5.4
(
CuAu
ainorganic diameter; bthickness of the organic shell; c
es are observed with this mixture.
dsmall+2tlsmall
)
/(dlarge+2tlarge); d tsmall/tlarge
;
eTwo additional binary liquid crystalline phas-
Binary NC Self-Assembly. In addition to single-
component superlattices, BNSL structures, several of
which are shown in Figure 5, are obtained by co-assembly
of two samples. More structures, including two binary
liquid crystal phases and unidentified structures, are re-
ported in the Supporting Information. (See Supporting
Information Figures S27-S35) The observed BNSLs en-
compass many structures observed in prior work includ-
ing phases isostructural with CuAu, Cu3Au, AlB2, NaZn13,
MgZn2, and CaCu5.49 Recent experimental48 and theoreti-
cal38,50 works conclude that soft sphere behavior induced
by organic ligands increases the number of equilibrium
BNSL phases, consistent with observed structural diversi-
ty.49 The formation of several different BNSL structures
using long polycatenar ligands allowed us to extend this
analysis. Following Horst and Travesset,38,50 the thermo-
dynamics of BNSL phases are modeled by a modification
of the power law equation above:
ꢋ
ꢉ
ꢃ ꢅ
ꢄ ꢆ ꢇꢌꢌꢇ
ꢀ
ꢁꢂ
̂
ꢁꢂ ꢈ ꢁꢂꢊ
ꢄ
Where ꢇ̂ represents interaction of the j and h NCs, as-
suming that ꢇꢌꢌ ꢆ 1. Figure 6 shows relevant equilibrium
ꢁꢂ
̂
Figure 6. Equilibrium phases of BNSLs for (a) p=6 and (b)
p=12, mapped as a function of size ratio ( ) versus interaction
phases for exponential values of p=6 and p=12 versus NC
size ratio γ, defined as the diameter (inorganic core plus
ligand shell) of the small NC divided by the diameter of
the large NC.50 Average values of inorganic diameters and
ligand lengths are obtained via TEM imaging. (See Table
1.)
γ
(εAB) or empirically-measured softness asymmetry parameter
(sAB). The equilibrium regions of each phase, indicated by
color at right, is shown with a solid line. The solid gray re-
gion represents the equilibrium state of phase separation of
the two components. Dots represent experimentally ob-
served BNSLs. Due to their similarity, the line for MgCu2 and
dots for MgZn2 are plotted in the same color. In those cases
of polymorphism from a given combination, the dots are
offset slightly for visual clarity. The value of c is 0.85 in (a)
and 1.0 in (b). Equilibrium lines from reference 50.
To map experimental results of this work on to the co-
ordinate of ꢇꢌ̂ ꢍ, the best correlation between experiment
and theory found in earlier results uses a coordinate of
ꢎꢏ ∙ ꢐꢌꢍ, where c is a scalar (1.0 for p=12; 0.85 for p=6) and
ꢐꢌꢍ is the softeness asymmetry parameter defined as50
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ligand shell thickness of small NC
ligand shell thickness of large NC
Supporting information containing additional synthesis
ꢐꢌꢍ
ꢆ
1
2
3
4
5
6
7
8
procedures and characterization data of organic compounds
and inorganic nanocrystals is in the Supporting Information
file. This material is available free of charge via the Internet
at http://pubs.acs.org.
We plot the experimental findings of this work in Fig-
ure 6 using colored dots, which indicate the BNSL struc-
ture. In general, the results are in substantial agreement
with theoretical predictions, although there are points of
difference. Our work shows previously-noted preferences
for non-equilibrium phases: where CsCl is predicted over
a large parameter space, the similar CuAu is observed in
our system.38 Also, MgZn2-type BNSLs, rather than
MgCu2, are found experimentally, although the energy
and structure difference between these phases is very
small, and we have therefore plotted them in the same
color in Figure 6. Although the bcc phases observed in the
single-component systems suggests a potential with p<7
for smaller NCs, in the BNSLs achieved from combina-
tions of these NCs, Figure 6 shows better agreement with
a p=12 exponent. This seems most likely because the po-
tential between larger particles, one of the constituents of
a binary system, is harder, as observed in single-
component self-assembly. Most points fall within ±0.1 in γ
or ꢐꢌꢍ (which also allows for measurement error) from the
equilibrium lines for the relevant phase. For example,
CuAu and MgZn2 points fall close or within the equilibri-
um regions of CsCl and MgCu2, respectively and most
other experimentally observed BNSLs are close to the
equilibrium regions for the observed phase. Where our
data differs substantially from the theoretical equilibrium
predictions is in the appearance of the Cu3Au BNSLs,
which appeared at much smaller values of γ, and in the
p=6 case lower values of ꢐꢌꢍ, than predicted. In several
cases, in fact, Cu3Au phases were observed at points in
phase space, especially for p=6, for which Li3Bi BNSLs are
the favored equilibrium phase. These data may provide
additional information for the refinement of models of
NC self-assembly and may hint at the necessity of adopt-
ing a more molecule-specific description of interparticle
interactions in some cases.51
AUTHOR INFORMATION
Corresponding Author
*cbmurray@sas.upenn.edu; bdonnio@ipcms.unistra.fr
9
Present Addresses
†Center for Nanoscale Materials, Argonne National Laborato-
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#Department of Chemical Engineering, Stanford University
Author Contributions
‡These authors contributed equally.
Notes
The authors declare a financial interest: aspects of this work
have been included in a U.S. provisional patent filing No.
62/310047.
ACKNOWLEDGMENT
The authors thank A. Travesset for helpful discussions and
access to pre-publication data and python scripts and K.
Weigandt for assistance running SANS experiments. This
work was supported by the CNRS-UPENN-SOLVAY through
the Complex Assemblies of Soft Matter Laboratory
(COMPASS), in partnership with the University of Pennsyl-
vania’s NSF MRSEC under Award No. DMR-112090. C.B.M.
acknowledges the Richard Perry University Professorship at
the University of Pennsylvania.
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