Nucleation kinetics vs chemical kinetics in the initial formation of semiconductor nanocrystals

Article abstract of DOI:10.1021/ja9063102

The initial formation of semiconductor nanocrystals/nanoclusters, that is, nucleation in the classic literature, was examined both theoretically and experimentally. An experimental method based on determining the initial reaction rate for the formation of

Full text of DOI:10.1021/ja9063102

Published on Web 09/23/2009
Nucleation Kinetics vs Chemical Kinetics in the Initial
Formation of Semiconductor Nanocrystals
Renguo Xie, Zheng Li, and Xiaogang Peng*
Department of Chemistry and Biochemistry, UniVersity of Arkansas,
FayetteVille, Arkansas 72701
Received July 28, 2009; E-mail: xpeng@uark.edu
Abstract: The initial formation of semiconductor nanocrystals/nanoclusters, that is, nucleation in the classic
literature, was examined both theoretically and experimentally. An experimental method based on
determining the initial reaction rate for the formation of nanocrystals/nanoclusters with fixed size and size
distribution was developed using InP and CdS nanocrystals/nanoclusters systems, especially the InP one.
This experimental strategy relies on the size-dependent absorption spectra of these semiconductor
nanoparticles as quantitative probes. The experimental results along with theoretical analysis indicate that
the classic nucleation model was unlikely relevant for such crystallization systems, whose bulk crystal
solubility in a solution is extremely low. Instead, the formation process was found to match a reaction-
controlled kinetics model. The results further imply that understanding of crystallization and development
of controlled synthesis of high quality colloidal nanocrystals are both closely related to identifying the
molecular mechanism and chemical kinetics.
Introduction
size regime, which is quantitatively expressed as the Gibbs-
Thompson equation (see below).5,6 In this classic picture, the
Crystallization is one of few most interesting yet mysterious
phenomena to human beings. The recent interest in nanocrystals
and other types of nanomaterials further illustrates the impor-
tanceofunderstandingcrystallizationinscienceandtechnology.1-4
In literature, nucleation refers to the initial formation process
of a crystal phase from another phase, usually a liquid, a
solution, or a gas phase. Nucleation defines the boundary
conditions for a given crystallization system and thus likely
dictates the following growth process under given temperature
and pressure. Unfortunately, study of nucleation process is a
grand challenge mostly because of the difficulty to quantitatively
determine the size and concentration of the newly formed tiny
clusters/nanocrystals.5,6 Quantum confined semiconductor nano-
clusters/nanocrystals (q-dots) are well-known for their strongly
size dependent optical properties in the size regime from a few
atoms to several millions of atoms.7 This work intends to
establish a method for studying the related nucleation processes
of q-dots. The experimental results from two q-dots systems,
InP (the main one) and CdS ones, were examined against the
theoretical models explored in this work.
continuous growth in size of crystals can only occur if the size
of the initial crystal embryo is larger than a given value, which
are called critical sized nuclei. In the solution, any crystals
smaller than the critical sized nuclei possess a thermodynamic
tendency to dissolve and any crystals larger than the critical
sized nuclei shall be thermodynamically driven to grow. This
inspired a kinetics model for nucleation proposed by Gibbs, with
the free energy difference between the monomers in solution
and the critical sized nuclei as the activation free energy. Though
this model has been widely adopted in literature, it often showed
at least a few magnitudes of difference from experimental
results.5,6,8
Thus, the theoretical challenge for understanding nucleation
is well-known to the field. However, lack of reliable and
systematic experimental data in the early stage of a crystalliza-
tion system implies that there are no sufficient insights for
solving such a challenge. In the field of colloidal nanocrystals,
scientists have started to pay attention to the nucleation
stage.9-11 However, to our knowledge, systematic and quantita-
tive studies on nucleation of colloidal nanocrystals are yet to
emerge, which requires systematic variation of reaction tem-
perature and reactant concentrations. Specifically for semicon-
ductor nanocrystals, their unique size-dependent optical prop-
erties offer unique probes for studying crystallization as
mentioned above. However, these studies are largely on the
The classic theory of crystallization in solution is largely built
on the fact that the solubility of a crystal with defined lattice
structure and composition increases drastically in the nanometer
(1) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Annu. ReV. Mater. Sci.
2000, 30, 545–610.
(2) Tian, Z. R.; Voigt, J. A.; Liu, J.; McKenzie, B.; McDermott, M. J.;
Rodriguez, M. A.; Konishi, H.; Xu, H. Nat. Mater. 2003, 2, 821–
826.
(8) Erdemir, D.; Lee, A. Y.; Myerson, A. S. Acc. Chem. Res. 2009, 42,
621–629.
(3) Xia, Y. N.; Yang, P. D.; Sun, Y. G.; Wu, Y. Y.; Mayers, B.; Gates,
B.; Yin, Y. D.; Kim, F.; Yan, Y. Q. AdV. Mater. 2003, 15, 353–389.
(4) Peng, X. G. Nano Res. 2009, 2, 425–447.
(9) Qu, L.; Yu, W. W.; Peng, X. Nano Lett. 2004, 4, 465–469.
(10) Kwon, S. G.; Piao, Y.; Park, J.; Angappane, S.; Jo, Y.; Hwang, N. M.;
Park, J. G.; Hyeon, T. J. Am. Chem. Soc. 2007, 129, 12571–12584.
(11) Rempel, J. Y.; Bawendi, M. G.; Jensen, K. F. J. Am. Chem. Soc. 2009,
131, 4479–4489.
(5) Mullin, J. W. Crystallization, 3rd ed.; 1997.
(6) Oxtoby, D. W. Acc. Chem. Res. 1998, 31, 91–97.
(7) Brus, L. E. J. Chem. Phys. 1984, 80, 4403–4409.
9
10.1021/ja9063102 CCC: $40.75  2009 American Chemical Society
J. AM. CHEM. SOC. 2009, 131, 15457–15466 15457

A R T I C L E S
Xie et al.
growth of the nanocrystals, and there are still plenty of
challenges for one to quantitatively probe a nucleation process.4
This work designed a series of experiments mostly for the
InP q-dots system in hopes of answering a few fundamental
questions quantitatively on nucleation, or more precisely,
formation of InP nanoclusters/nanocrystals. These questions
include the validity of critical size nuclei, the effects of monomer
concentration, the effects of ligands and other additives, and
the effects of temperature. The key feature of the experimental
method is to enable quantitative measurements by generating
nanoclusters/nanocrystals with fixed size and size distribution
in a reasonably broad experimental window. A theoretical
section will be presented to examine options for understanding
the experimental data to be described.
Here, ω is defined as supersaturation, which is the ratio
between the monomer concentration and the bulk solubility
([M]/S∞). In eq 4, the first term is positive. If ω is not greater
than 1, ∆G will be always greater than zero and formation of
crystals shall be thermodynamically prohibitive. Consequently,
any crystals in the solution will dissolve. When ω is greater
than 1, ∆G becomes negative when the size of the crystal is
larger than the particles with its solubility equal to the given
monomer concentration, whose size will be named de. At the
same time, eq 4 tells us that, when d ) 0, ∆G is also zero.
Mathematically, one maximum shall exist between two nodes,
de and d ) 0. Let the derivative of ∆G equals to zero. This
gives the critical sized nuclei (d*) (eq 5) and the corresponding
critical Gibbs free energy of nucleation (∆G*) as eq 6.
Theoretical Section
8σVm
3RTInω
d* )
(5)
(6)
Classic Nucleation Theory. The classic nucleation theory has
its roots in the Gibbs-Thompson equation (eq 1). In this
subsection, we will try to discuss an approach different from
the most popular one presented in literature which was originally
derived by Gibbs.5,6 Because of the increased surface-to-volume
ratio, the chemical potential of a crystal increases rapidly as its
size decreases. Consequently, its solubility increases as its size
decreases following the Gibbs-Thompson equation (eq 1).
128πσ3V2m
(9RTInω)2
∆G* )
∆G* is considered as the activation free energy according to
the Gibbs nucleation theory. Following the strategy proposed
by Gibbs, the nucleation kinetics equation emerges as eq 7,
provided that the particle concentration is defined as [P] and
the formation rate of particles (d[P]/dt) is represented as r.
Sd ) S∞exp(4 σVm/dRT)
(1)
-128πσ3V2m
(9Inω)2(RT)3
where Sd and S∞ are the solubility values of a crystal with its
size (or diameter) as d and the corresponding bulk crystal,
respectively. σ is the specific surface energy, and Vm is the molar
volume of the crystal. R is the gas constant, and T is the absolute
temperature. The Gibbs-Thompson equation assumes a spheri-
cal shape for crystals, which will be adopted in most parts of
this work unless it is pointed out otherwise.
Thermodynamically speaking, eq 1 tells us that the chemical
potential of a given-sized crystal equals to that of the monomers
with their concentration being the solubility of the crystal.12
This means that if µd and µo are, respectively, the chemical
potential of a crystal with its size as d and the standard chemical
potential of the monomers under the given conditions, we should
have the following relationship.
r ) d[P]/dt ) A exp
(7)
and
128πσ3V2m
(9lnω)2(RT)3
In(r) ) In(A) -
(7a)
It should be pointed out that the most popular method to yield
nucleation kinetics equations derived by Gibbs followed a
geometric argument of the free energy change, which includes
a positive term as the surface free energy and a negative term
as the crystal interior part.5,6 That method is direct, and the
results are qualitatively the same as those presented in eqs 5-7.
However, Gibbs equations are not self-consistent. For example,
the crystal in equilibrium with the monomers in the solution,
namely de, suggested by that model is different from the
Gibbs-Thompson equation, although the method must apply
the Gibbs-Thompson equation at some point in the deduction.5
The resulting critical sized nuclei (d*) in the Gibbs method is
simply the crystal with its solubility equal to the monomer
concentration in the solution (de) calculated from eq 1. This
implies that either the Gibbs-Thompson equation or the classic
nucleation kinetics equations should be modified. This work
chose to stick to the Gibbs-Thompson equation simply because
this equation has been widely accepted and used in fields of
crystallization, surface science, etc. A more in depth theoretical
argument is in development and shall be a part of a separate
publication.
µd ) µo + RTInSd ) µo + RT(InS∞ + 4σVm/dRT) (2)
For any monomer concentration represented as [M], the
chemical potential of monomers in the solution (µM) can be
expressed as eq 3.
µM ) µo + RTIn[M]
(3)
Formation of a crystal with its size as d from the monomers
with their concentration being [M] shall involve a free energy
change (∆G) that should be calculated using eq 4. In eq 4, n is
the total number of moles of the monomer units in the crystal,
which is πd3/(6Vm) for the crystal with its size as d.
πd3RT(InS∞ + 4σVm/dRT - In[M])
Quantitatively, the critical sized nuclei found in the Gibbs
method are 1/3 larger in size (diameter) than the valve shown
in eq 5. Although with this quantitative discrepancy, the main
conclusion drawn in this report does not change using the
equations obtained from either of the two methods.
∆G ) n(µd - µM) )
)
6Vm
2πσd2
3
πd3RTInω
6Vm
-
(4)
Bulk Solubility. Bulk solubility, the term used in the above
discussions, S∞, needs to be clarified for determining ω, d*, and
(12) Peng, Z. A.; Peng, X. J. Am. Chem. Soc. 2002, 124, 3343–3353.
9
15458 J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009

Nucleation Kinetics vs Chemical Kinetics
A R T I C L E S
∆G*, which is critically related to the solution conditions. By
definition, it can be calculated from the solubility equilibrium
constant (Ksp) of a given compound. Using InP as an example,
the related chemical equilibrium should be as follows.
be pointed out that although the specific surface free energy
(σ) is known to be related to the possible surface adsorbents,
the influence of solution environment on S∞ is substantially more
comprehensive. For example, related to the current system, the
supersaturation should change substantially by varying the
concentration of the fatty acid additives. This is so because the
solubility of a given sized InP nanocluster/nanocrystal would
increase dramaticallyswith a cubic functionsby increasing the
fatty acid concentration (eq 11). From a different perspective,
the theoretical results in this subsection explain why ligands
effects could be more substantial for monomers than that for
the resulting nanocrystals.14
Limitations of Classic Nucleation Kinetics Model. The limita-
tions of the classic nucleation kinetics model discussed above
can be identified by going through the mathematic procedure.
First, the Gibbs free energy barrier in eq 7 depends strongly on
the monomer concentration, which is fundamentally different
from the activation energy in chemical kinetics. Even if this
model is correct, it is unlikely to identify a fixed size for critical
sized nuclei and activation Gibbs free energy barrier (eqs 5 and
6), provided the rapid temporal change of the monomer
concentration in practical synthesis. Second, the Gibbs free
energy barrier identified by eq 6 is a thermodynamic barrier,
instead of a kinetics barrier. It is quite possible that the formation
of crystals may involve some common chemical reactions, such
as formation of the structural unit (InP molecule in our example),
the reaction occurred on the surface of a crystal embryo, and
the diffusion of reactants, etc. As a result, if one of the chemical
processes involved in nucleation is very slow, the entire
nucleation might become reaction-controlled and the nucleation
kinetics shown by eq 7 might not play much of a role at all.
From a pure thermodynamic standpoint, the nucleation
kinetics presented above could have some significant limitations
as well. This can be readily demonstrated by estimating the
critical sized nuclei using eq 5.
There are barely any constants available to do such estimation
in a practical nonaqueous synthetic system at this moment. For
illustration of the principle, one can use an aqueous system to
support the argument. Let us take the most common semicon-
ductor nanocrystals, CdSe ones, as the example. The Ksp for
CdSe is 6.3 × 10-36. The Ka for typical fatty acids, such as
acetic acid, and the Ka for H2Se (the first- and second-step
combined value) are 1.5 × 10-5 and 1.3 × 10-15, respectively.
Thecomplexstabilityconstantofcadmiumfattyacidsaltscadmium
acetate in this casesis found to be 1.4 × 103. The fatty acid
concentration and cadmium fatty acid salt concentrations are
both assumed to be 0.1 mol/L. For the specific surface free
energy, let us take a relatively high end value used in the
Talapin’s report,15 0.5 J/m2. This roughly corresponds to 50 000
J/mol for the free energy difference between a Se-Cd bond
and a RCOO-Cd bond.
With all of the data offered in the above paragraph, one can
calculate the size of the critical sized nuclei for CdSe in this
specific system at 298 K to be 0.29 nm. This is slightly smaller
than the length of a single Cd-Se bond, which means that the
basis of nucleation kinetics does not exist at all. In other words,
there appears to be no free energy barrier for the formation of
CdSe crystals/clusters with any size, even if the clusters are
(CdSe)2 and (CdSe)3. It should be pointed out that, under the
acidity specified above, it is more proper for H2Se to ionize
(InP)bulk T In3+ + P3-
(8)
The Ksp of typical III-V and II-VI semiconductor compound
is extremely small in aqueous solution. In nonpolar solutions,
the ions are even more unstable. With the existence of ligands
and other additives, however, the above equilibrium would be
modified substantially. Typically, fatty acids (HFA) are common
ligands, which shall establish a new equilibrium with InP
crystals.
(InP)bulk + 3HFA T In(FA)3 + H3P
(9)
The chemical equilibrium constant for this equilibrium (eq
obv
9) can be regarded as the Ksp observed in experiments, Ksp.
[In(FA)3][H3P]
obv
K
)
)
sp
[HFA]3
[H+]3[FA-]3
[HFA]3
[In(FA)3]
[H3P]
[In3+][P3-]•
•
•
)
[In3+][FA-]3 [H+]3[P3-
]
Ksp·(HFAKa)3·In(FA) Ks
3
(10)
H PKa
3
Here, HFAKa and H PKa are respectively the acid dissociation
3
constants of HFA and H3P, and In(FA) Ks is the complex stability
3
constant of the indium fatty acid salt (In(FA)3). Equation 10
obv
implies that, in most experiments,
K is a complex combina-
sp
tion of several chemical equilibrium constants, which is the
thermodynamic root for the strong influence of solution environ-
ment on a crystallization system. This has recently been noticed
both experimentally13,14 and theoretically11 in the field of
colloidal nanocrystals.
Practically, solubility of a compound should be measured
using a chosen component. In this report and the others related
to the synthesis of high quality compound semiconductor
nanocrystals, the cationic precursor is often in a large excess
because the ligands are typical for the surface cations. Thus, it
is more convenient to choose the anions as a measurement of
the solubility. For InP system, we express the solubility of InP
crystal using the concentration of the phosphors monomers. For
simplicity, let us use H3P as the representative of all possible
phosphors monomers in the solution. From eqs 9 and 10, the
solubility of bulk InP can be calculated using the following
equation.
[HFA]3
S∞ ) [H3P] ) obvK
)
sp[In(FA)3]
Ksp·(HFAKa)3·In(FA) Ks
3
[HFA]3
[In(FA)3]
•
(11)
H PKa
3
Equation 11 implies that, because of the direct dependence
of the solubility (or chemical potential) of nanoclusters/
nanocrystals on S∞, a crystallization system must be considered
by taking into account of the solution environment. It should
(13) Yu, W. W.; Peng, X. Angew. Chemie, Int. Ed. 2002, 41, 2368–2371.
(14) Yu, W. W.; Wang, Y. A.; Peng, X. Chem. Mater. 2003, 15, 4300–
4308.
(15) Talapin, D. V.; Rogach, A. L.; Haase, M.; Weller, H. J. Phys. Chem.
B 2001, 105, 12278–12285.
9
J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009 15459

A R T I C L E S
Xie et al.
tor nanoclusters/nanocrystal system yet probably because of less
interest in this size regime in comparison to the noble metal
ones. Fundamentally, noble metal atoms should be extremely
insoluble in the reported reaction conditions,18,19 typically
aqueous solutions. Following the same argument offered above,
it would be very easy to establish a monomer concentration
that is substantially higher than the maximum solubility of such
tiny molecular clusters, such as dimers and trimers.
Overall, the above discussions imply that, for very insoluble
crystal systems, the monomer concentration in the solution could
reach a value higher than the solubility of the smallest possible
molecular/cluster species, such as a dimer and trimer. Therefore,
in such systems, nucleation kinetics will unlikely play a
significant role in the formation of nanoclusters/nanocrystals.
Kinetically speaking, this means that the rate-determining step
in the formation of such crystals will be chemical reaction(s).
The plot shown in Figure 1 offers a complete picture for the
above discussions. In the plot, the red curve is a modified version
of the Gibbs-Thompson equation (eq 1). Two possible “magic
sized clusters”spresumably between 1-2 nm in sizesare
represented as two free energy minima in the curve, and the
dashed part implies that these molecular clusters (<∼1 nm) have
very distinct structures from the bulk crystal and should have
substantially smaller solubility than that predicted by the
Gibbs-Thompson equation. The maximum solubility (Smax) of
the system is the solubility of the smallest molecular clusters,
possibly a dimer, a trimer, etc., and S∞ is the solubility of the
bulk crystals as defined above. The entire plot area is divided
into three regions by Smax and S∞. The bottom region is simply
the dissolution of crystals, which does not need to be discussed
in this report.
The top region in Figure 1 represents the “reaction-controlled
formation” region, in which the monomer concentration in the
solution is higher than the maximum solubility of the system.
Because of the extremely high supersaturation, formation of
clusters/crystals is thermodynamically favorable for all sizes and
no thermodynamic barrier exists to define critical sized nuclei.
However, because of the existence of the magic sized clusters
in the 1-2 nm size range (see the schematic drawing in Figure
1), the initially formed tiny molecular clusters could grow into
one of those magic sized clusters and be trapped thermodynami-
cally. This allows us to determine the particle concentration and
formation rate of the particles as demonstrated in this work.
These nanoclusters could be dissolved slowly by the solution
additives such as a high concentration of fatty acids, which has
been known as “backward tunneling”.12 The condition needed
for “backward tunneling” is that the monomer concentration in
the solution is below the solubility of the “magic sized cluster”,
which thermodynamically drives the complete dissolution of
the cluster by going through the free energy barrier at the small
size side. Alternatively, a high monomer concentration/temper-
ature could help the magic sized clusters to overcome the free
energy barrier at their large size side and grow to a large one,
which is the “forward tunneling”.12 The combination of “forward
tunneling” and “backward tunneling” serve as the basis of “self-
focusing” related to nanoclusters.20
Figure 1. Formation of nanoclusters/nanocrystals. Smax and S∞ at the right
side of the plot are the maximum solubility of the clusters/crystals with the
smallest possible number of structural units and the bulk crystal, respectively.
only to HSe- ion, instead of Se2- ions. This shall further reduce
the critical sized nuclei calculated using eq 5.
The conclusion drawn in the above paragraph is substantial
because it implies that, even from a pure thermodynamic
viewpoint, the classic nucleation kinetics might not withstand
at all. To better comprehend this conclusion, there are two issues
that need to be discussed. It has been well-known that, within
1-2 nm size range, stable nanoclusters are “magic sized
clusters”, which have a perfect close-shell atomic configura-
tion.16 Their outstanding stability in comparison to the nano-
clusters with similar sizesseither slightly smaller or slightly
larger than the given magic sizesimplies that their solubility
should be noticeably smaller than that estimated above (see
Figure 1).12 Furthermore, theoretical and experimental results
both revealed that clusters smaller than ∼1 nm are substantially
differentiated from the crystal lattice structure. For example,
gold clusters up to 18 atoms were found to be flat or hollow
cages.17 This means that the Gibbs-Thompson equation (eq 1)
overestimates the equilibrium monomer concentration for very
small molecular clusters. In other words, the calculated critical
sized nuclei would be further unrealistic in size.
The second issue is regarding experimental observations
related to the validity of critical sized nuclei. Molecular dimers
and trimers of noble metals, such as Ag2 and Ag3, have been
observed to form readily in experimental systems by several
research groups.18,19 It is interesting to notice that such
molecular clusters could only be isolated under very mild
reaction conditions, such as relatively weak visible light and
with proper stabilizers in place.19 Otherwise, formation of large
sized crystals would inevitably occur. Furthermore, the results
from the Xia group suggested that these tiny molecular clusters
determined the final crystal concentration in the solution and
could thus be considered as “nuclei” of the system.18 Such
strongly supportive results for stable existence of molecular
dimers and trimers have not been observed for the semiconduc-
The middle region in Figure 1 is the “nucleation-controlled
formation”, which is the main model considered in the classic
nucleation literature. In this region, the monomer concentration
is lower than the maximum solubility of the smallest molecular
clusters in the system but higher than the solubility of the bulk
(16) Herron, N.; Calabrese, J. C.; Farneth, W. E.; Wang, Y. Science 1993,
259, 1426–1428.
(17) Bulusu, S.; Li, X.; Wang, L. S.; Zeng, X. C. Proc. Natl. Acad. Sci.
U.S.A. 2006, 103, 8326–8330.
(18) Xia, Y.; Xiong, Y. J.; Lim, B.; Skrabalak, S. E. Angew. Chem., Int.
Ed. 2009, 48, 60–103.
(19) Diez, I.; Pusa, M.; Kulmala, S.; Jiang, H.; Walther, A.; Goldmann,
A. S.; Muller, A. H. E.; Ikkala, O.; Ras, R. H. A. Angew. Chem., Int.
Ed. 2009, 48, 2122–2125.
(20) Xie, R. G.; Peng, X. G. Angew. Chem., Int. Ed. 2008, 47, 7677–7680.
9
15460 J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009

Nucleation Kinetics vs Chemical Kinetics
A R T I C L E S
crystals. A critical sized nucleus for a given monomer concen-
tration could thus be defined by eq 5 or its variations as
discussed above. As a result, formation of a crystal must go
through a free energy barrier, which is the homogeneous
nucleation accounted by eq 7. As the monomer concentration
approaches the solubility of the bulk crystals, homogeneous
nucleation needs to overcome a very substantial free energy
barrier. Subsequently, heterogeneous nucleation becomes the
dominating path, which could be used for growth of hierarchical
nanostructures on various substrates.2
It should be pointed out that, in this region, initial formation
of crystals might still not be nucleation-controlled if there is a
very slow chemical process involved (see the first paragraph in
this sub-section). In this case, the overall rate of formation would
be slower than that predicted by eq 7.
Chemical Kinetics. The chemical kinetics for the “reaction-
controlled formation” region in Figure 1 can be empirically
presented by eq 12, with k as the reaction kinetics constant and
using the InP system studied here as an example.
Figure 2. (a) and (b) Absorption spectra of InP nanoclusters formed with
different precursors/ligands (HHe ) hexanoic acid, HMy ) myristic acid)
and reaction temperatures. (c) Size dependent absorption peak position of
InP nanocrystals adopted from reference with a numerical fitting. (d) Molar
particle extinction coefficient of InP nanocrystals vs the size of the
nanocrystals adopted from reference.
r ) d[P]/dt ) k[In(FA)3]a[P(TMS)3]b[acid]c
(12)
unified way to represent them: for a given acid, it would be
written as a capitalized “H” combined with the capitalized first
letter and the low-case second letter of the common name of
the acid. The capitalized “H” will be removed for the corre-
sponding carboxylate. For example, myristic acid and indium
myristate should be written as HMy and In(My)3, respectively.
This system is consistent with the abbreviation of acetic acid
and the corresponding salts. All of the fatty acids used in this
work are summarized in the Supporting Information with their
abbreviations.
This choice of the main reaction system was mainly based
on the fact that, as shown in Figure 2 (a and b), InP formed
small nanoclusters in a quite broad temperature range with
different precursors/ligands in this specific reaction system. In
addition, unlike typical II-VI semiconductor nanocrystal sys-
tems, the involved reaction for the formation of InP in a similar
reaction system was identified previously.22,23 An inorganic salt
(InCl3), instead of indium fatty acid salts, was used in the
previous reports, and the reaction was proposed as a simple
exchange reaction between P(TMS)3 and the indium salt (indium
chloride) to yield InP and Cl-TMS. It is reasonable to assume
that a similar reaction occurred in the current system.
Because the ligands used were all for cationic surface atoms
in the reaction system, all reactions were performed with a large
excess of indium precursors unless specified otherwise. Excess
indium fatty acid salts helped to maintain colloidal stability of
the InP nanoclusters. If a considerable amount of fatty amines
were present, however, it was not necessary to maintain an
excess amount of indium fatty acid salts.
The size of the nanoclusters shown in Figure 2a and b is
slightly larger than 1 nm (Figure 2c) and only has 10-20
structural units (single InP unit) per particle, which should be
a “magic sized nanocluster”. Their extremely small size makes
them be much better qualified as “nuclei” than what have been
discussed in the classic theory, greater than tens of nanometers
in size.8 The constant size and size distribution under a broad
In Equation 12, a, b, and c are the reaction orders of the
corresponding reactants. If some other chemicals are involved
in the reaction, more concentration terms should be included.
If the reaction obeys Arrhenius kinetics, k can be written as a
function of the reaction temperature, activation energy (Ea), and
pre-exponential factor (A).
k ) Ae-Ea/RT or In(k) ) In(A)-Ea/RT
(13)
The pre-exponential factor in eq 13 is known to be related to
activation entropy of a given reaction.21 Combining eqs 12 and
13, we have the following general equation:
ln(r) ) ln(A) - Ea/RT + a ln[In(FA)3] + b ln[P(TMS)3] +
c ln[acid] (14)
It should be pointed out that eqs 12, 13, and 14 only account
the formation of nanoclusters/nanocrystals. If growth of the
crystals is also of consideration, some modifications would be
needed. There are some significant distinctions between eqs 7
and 14. For example, the formation rate of nuclei is extremely
sensitive to the monomer concentration in eq 7. In the formation
of Fe3O4 nanocrystals in a similar solvent system used in this
work, Kwon et al.10 estimated that the nucleation rate shall
increase 10190 by just increasing supersaturation from 2 to 10.
This is so because the monomer concentration is in the
exponential term in eq 7. Furthermore, eqs 7 and 14 indicates
a very different temperature dependence of the formation rate.
As described below, these differences are so substantial that it
becomes easy to distinguish one type of kinetics from the other.
Experimental Results
Main Reaction System. The main reaction system used in
this work was InP nanoclusters/nanocrystal system initiated by
injecting tris(trimethylsilyl)phosphine (P(TMS)3) into a hot
octadecene (ODE) solution containing indium fatty acid salts
and free fatty acid at a given reaction temperature. Fatty acids
and the corresponding caroboxylates with different chain length
were used widely in this work and also in synthesis of high
quality nanocrystals in general. For simplicity, we suggest a
(22) Micic, O. I.; Sprague, J. R.; Curtis, C. J.; Jones, K. M.; Machol, J. L.;
Nozik, A. J.; Giessen, H.; Fluegel, B.; Mohs, G.; Peyghambarian, N.
J. Phys. Chem. 1995, 99, 7754–7759.
(23) Guzelian, A. A.; Katari, J. E. B.; Kadavanich, A. V.; Banin, U.; Hamad,
K.; Juban, E.; Alivisatos, A. P.; Wolters, R. H.; Arnold, C. C.; Heath,
J. R. J. Phys. Chem. 1996, 100, 7212–7219.
(21) Atkins, P. W. Phys. Chem., 6th ed.; 1998.
9
J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009 15461

A R T I C L E S
Xie et al.
Figure 3. Monomer concentration ([P(TMS)3]) vs InP nanoclusters
concentration ([P]). The solid line is a linear fitting of the results with the
fitting function in the plot. Reaction conditions: 0.4 mmol In(He)3, 1.2 mmol
HHe, 4 mL ODE, T ) 158 °C.
spectrum of reaction conditions provides two interesting features.
First, it largely eliminates experimental errors for determining
reaction order and activation energy (see details below). Second,
it sets aside the size dependent properties of the nuclei, which
could substantially complicate the interpretation of the results
because of the drastically different yet unknown relationship
between different sized nanolcusters and their supersaturation
concentrations. It should be pointed out that formation of such
small sized nanoclusters as the initial species is not uncommon.
For example, InAs system was actually found to be too difficult
to avoid the formation of such nanoclusters in the initial stage.20
The extremely small size of the nanoclusters could not be
determined directly by transmission electron microscope. For-
tunately, both size and molar extinction coefficient (ε) of InP
nanocrystals with relatively large sizes were determined by the
Weller’s group (Figure 2c and d).24 We carried some additional
measurements and found that our results were within the same
range. We fitted the data points into numerical functions (Figure
1c and d), which gave us the means to calculate the size and
extinction coefficient of the nanoclusters. The size is about 1.1
nm and with about 14 InP units in each nanocluster. From the
absorption spectra shown in Figure 2a and b, the InP nanoclus-
ters were unlikely monodispersed. However, the identical peak
position and spectral contour indicate that the size and size
distribution of the nanoclusters obtained were constant under
the reaction conditions specified.
Minimum Concentration of P(TMS)3 for the Formation of
InP Nanoclusters. The minimum concentration of P(TMS)3 for
the formation of InP nanoclusters was determined under various
conditions. Figure 3 illustrates one series of data, which shows
that the InP nanoclusters concentration decreased as the initial
concentration of P(TMS)3 decreased. The reaction conditions
were identical for this set of reactions except the variation of
the initial concentration of P(TMS)3. The particle concentration
was measured after each reaction proceeded for a sufficient
amount of time (∼20 s). UV-vis measurements verified that
the size and size distribution of the InP nanoclusters in all
reactions were almost identical to those shown in Figure 2 (a
and b).
The experimental data points in Figure 3 can be well fitted
into a linear function (see the fitting function in Figure 3). The
fitting line was extrapolated to the particle concentration equals
to zero. This gave us the minimum [P(TMS)3] as 5.8 mmol/L,
at which no particles could be formed. This value was found to
be consistent with the experimental results. Although the particle
concentration could not be determined with the same confidence
Figure 4. Initial formation rate of nanoclusters vs the concentration of
limiting monomer, P(TMS)3. (Top) Plot as chemical kinetics. (Bottom) Plot
as classic nucleation kinetics. Reaction conditions: 0.4 mmol In(He)3, 1.2
mmol HHe, 4 mL ODE, T ) 158 °C.
as the data shown in Figure 3, when [P(TMS)3] was 10 mmol/
L, formation of InP nanoclusters was indeed observed. However,
when the [P(TMS)3] decreased to 5 mmol/L, InP nanoclusters
could not be detected by UV-vis measurements no matter how
long time the reaction was maintained.
The existence of a minimum [P(TMS)3] means that, below
this concentration, no formation of the nanoclusters occurred
in the system under the given reaction conditions. Given the
constant size and size distribution of the nanoclusters for all
reactions, the minimum [P(TMS)3] could be regarded as the
solubility of the given sized nanoclusters. Such an assignment
may overestimate the solubility, but it should be at least the
upper limit value, which is sufficient for justifying the related
analysis later.
With the size and solubility of a given sized nanocluster
known, the bulk solubility of InP in the given solution system
associated with Figure 3 can be estimated using eq 1 combined
with eq 11. Assuming 0.5 J/m2 as the specific surface free
energy15 and reaction temperature being 451 K, the obtained
value for S∞ is 1.9 × 10-8 mol/L. The solubility values discussed
here are all based on the phosphorus monomers. As shown by
eq 11, such a relatively high bulk solubility is due to the
existence of a decent concentration of free fatty acid, which
stabilized the ionization products of InP crystals as H3P and
indium fatty acid salts (eq 9), especially by converting a very
unstable P3- to a very stable H3P.
Reaction Order. The reaction order for the formation of InP
nanoclusters was determined for phosphorus precursor, indium
precursor, fatty acids, and amines separately. In the reactions
without amines added, the P(TMS)3 was the limiting precursor
as mentioned above. The top plot in Figure 4 shows that the
initial formation rate of the nanoclusters could be well fitted
according to eq 14 against the concentration of P(TMS)3. The
reaction order can be obtained as the slope of the ln(r) -
ln[P(TMS)3] plot, which is practically equal to one. Although
the sizes of the CdSe nanocrystals varied from one reaction to
another, the previous in situ studies of the formation of CdSe
nanocrystals also recorded a first order relationship between the
concentration of the nanocrystals and the monomer concentra-
tion.9
(24) Haubold, S.; Haase, M.; Kornowski, A.; Weller, H. ChemPhysChem
2001, 2, 331.
9
15462 J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009

Nucleation Kinetics vs Chemical Kinetics
A R T I C L E S
no amines were added in the reaction solution, changing the
concentration of fatty acids did not change the size and size
distribution of the InP nanoclusters. Because the reaction order
was negative one, fatty acids should promote the dissolution of
the InP nanoclusters, or the “backward tunneling” of the
nanoclusters discussed above.12 Consistent with this, this
dissolution process seemed to be quite slow. For the reaction
with the highest acid concentration in Figure 5, if the reaction
was allowed to proceed for about 20 min or longer, the
nanoclusters would gradually disappear. Furthermore, in all
reactions, if a significant amount of fatty acid was added after
the formation of the InP nanoclusters, the nanoclusters could
be completely dissolved slowly.
The amine-added reactions yielded large InP nanoclusters
with some variation in their size and size distribution (see details
below). The reaction rate for the formation of the InP nano-
clusters did not show a monotonic trend against the amine
concentration (Figure S3, Supporting Information). This was
not considered to be completely surprising. In literature, the
roles of fatty amines were found to be complex, including
formation of a complex with indium ions to slow down the
reaction rate, activation of metal fatty acid salts through the
formation of amides, coordination to the surface of the nano-
clusters/nanocrystals, formation of salts with fatty acids to
indirectly activate the reaction, etc. Presumably, by changing
their concentration, each of these roles of amines may have a
different weight in the whole reaction scheme, which ended up
a nonmonotonic relationship between the formation rate of the
nanoclusters and the concentration of the amines. In addition,
these complex roles could also complicate the reaction paths
and might cause the dramatic change of the reaction orders
against the precursors discussed above.
Temperature Dependence of the Formation Rate of the
InP Nanoclusters. The temperature dependence of the formation
rate of the InP nanoclusters was determined under a variety of
conditions. Figure 6 illustrates the results for the reactions
without the addition of amines by varying the chain length and
concentration of the fatty acids. The experimental results could
be well fitted with the chemical kinetics equation (eq 14). In
such a ln(r) - 1/(RT) plot, the activation energy can be obtained
as the slope of the linear fitting as shown by eq 14. To maintain
the same nanocluster size and size distribution, the reaction
temperature ranges may differ from one series to another.
According to eq 14, however, this should not affect the
determination of the activation energy (Ea).
The activation energy was found to be the same in the reaction
series for the same type of fatty acid with different acid
concentrations, namely, 6.3 ( 0.3 (KJ/mol) for butaoic acid,
9.1 ( 0.3 (KJ/mol) for hexanoic acid, and 10.7 ( 0.3 (KJ/mol)
for octanoic acid. This means that the activation energy
increased as the increase of the chain length of the acids (Figure
6, right).
Figure 5. Initial formation rates of the InP nanoclusters vs the acid
concentration (HHe). Reaction conditions: 0.4 mmol In(He)3, 0.2 mmol
P(TMS)3, 4 mL ODE, T ) 158 °C.
The discussion in the above paragraphs also reveals that the
increase of the formation rate of nanoclusters as the increase of
the monomer concentration would be too slow to be explained
using the classic nucleation theory. To further illustrate this
point, the experimental results were replotted (Figure 4 bottom)
using the nucleation kinetics equation (eq 7a). The supersatu-
ration (ω) for a given reaction was calculated by using the bulk
solubility measured against [P(TMS)3] (see Figure 2 and the
related text). The fitting was slightly worse than that using eq
14. The pre-exponential factor (A) for the nucleation kinetics
was calculated as 1.24 using the intercept in the plot (see eq
7a), which is unreasonably small for a solution reaction. The
most striking discrepancy was found for the slope of the fitting.
From the slope of the plot (Figure 4, bottom), the specific surface
free energy was calculated to be 25 000 000 (J/m2), which is
about 7 magnitudes larger than what could be expected.15 The
bulk solubility estimated above (see Figure 2 and the related
text) was an upper limit value. By referring to eq 7, one would
expect an even larger discrepancy using a lower bulk solubility
in calculating supersaturation. In any case, such a large
discrepancy was often noticed in literature,6 which implies that
the nucleation kinetics equation does not work for the current
system.
The concentration effect of indium precursors was found to
be small in the reactions without the addition of amines because
such reactions needed to be run under excess indium precursor
conditions. With a large excess of amine in place, the formation
rate of InP nanoclusters was determined to be the third order
against the concentration of indium precursors (Figure S1,
Supporting Information). The existence of amines also affected
the reaction order of P(TMS)3, from the first order without amine
(Figure 4, top) to the second order with amine (Figure S2,
Supporting Information). As discussed below, the sizes of the
InP nanoclusters were found to be less constant and slightly
larger than the ones shown in Figure 2 (see detail below).
However, although the reaction orders were different for the
reactions with and without amines, the general conclusion was
the same, that the formation kinetics could be well fit with the
regular chemical kinetics (eq 14), instead of nucleation kinetics
(eq 7).
The reaction order of additives for the formation of nano-
clusters was also studied. Fatty acids have been widely used as
an additive in synthesis of high quality colloidal nanocrystals
in organic solvents after the introduction of the “greener
approaches”.4 It was found that, for the case of CdS nanocryst-
als,13 fatty acids reduced the consumption rate of precursors in
the nucleation stage but not the growth stage. Consistent with
this, the results in Figure 5 reveal that, for InP q-dot system,
the formation rate of the given sized nanoclusters was found to
be inverserly proportional to the acid concentration, negative
one as the reaction order. It should also be pointed out that, if
Although the activation energy was the same for the same
type of acid by varying the acid concentration (see Figure 6
left and middle plots as examples), the intercept decreased
systematically as the acid concentration increased. This matched
the reaction order well for fatty acid determined above (Figure
5). According to eq 14, for a given type of acid, the difference
between two different acid concentrations in Figure 6 should
only be the acid concentration term, -ln[acid]. Because the
reaction was found to be negative first-order against fatty acid
concentration (Figure 5), the difference of the y-axis intercepts
between two lines in Figure 6 (either left or middle plot) could
9
J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009 15463

A R T I C L E S
Xie et al.
Figure 6. Irving plots of the initial formation rate of the InP nanoclusters without amine in place. (Left) Reactions with indium butanate (In(BA)3) as the
precursor and different buranoic acid concentrations. (Middle) Reactions with indium haxanate (In(HA)3) as the precursor and different hexanoic acid
concentrations. (Right) Reactions with the acids of different chain-length but the same acid concentration. In all experiments, [In(FA)3] ) 0.08 mol/L,
[P(TMS)3] ) 0.04 mol/L.
tion of the metal fatty acid salts, however, was found to vary
substantially.25 As a result, the activation energy and pre-
exponential factors also changed significantly (Figure S4,
Supporting Information), reflecting a different reaction path. This
means that, if mixed ligands are used in a synthesis, the exact
precursor structure shall affect the formation kinetics substantially.
Temperature Dependence of the Reactions with Fatty
Amines Added As Additives. The temperature dependence of
the reactions with fatty amines added as additives was also
studied. The size of the nanoclusters formed with amine added
(Figure 7 right) was found to be larger and less constant under
Figure 7. (Left) Irving plot of the reactions with and without fatty amines
added. (Right) Absorption spectra of the InP nanoclusters formed at different
reaction temperatures with amine added. Reaction conditions: 0.4 mmol
In(Ac)3, 0.2 mmol P(TMS)3, 1.5 mmol HMy, 4 mL ODE.
different reaction temperatures than those generated in the
reactions without amines (Figure 2).
The results in Figure 7 (left) indicate that the addition of
amines in this temperature range increased the activation energy
substantially, which experimentally resulted in a significant
increase of the temperature dependence of the formation rate
of the InP nanoclusters. The pre-exponential factor also
increased upon the addition of the amines. These results could
be tentatively explained by the fact that fatty amines were found
to stabilize indium ions in nonpolar solvents under the reaction
conditions.26 A stable complex should increase activation energy
by decreasing the potential energy of the reactants. Because
amines are neutral ligands, the charges of the indium ions must
be balanced by the carboxylates. As a result, the indium
precursor becomes very complex in comparison to the original
indium fatty acid salts. When the transition state was formed
by the reaction of this complex indium precursor with the
phosphorus precursor, the activation entropy would be quite
large by releasing more molecules into the reaction solution.
Therefore, by adding fatty amines into the reaction system, an
increase of the activation entropy should be expected, which in
turn increased the pre-exponential factor according to the
Eyring’s equation.21
be readily calculated. The calculated values matched quite well
with the fitting results.
If the formation of the InP nanoclusters followed the classic
nucleation kinetics (eq 7), one should not expect the results
shown in Figure 6. The increase of acid concentration shall
substantially increase the bulk solubility (eq 11), which means
that the supersaturation should decrease as the concentration
of acid increased. For example, when hexanoic acid concentra-
tion increased from 0.20 to 0.28 mol/L without changing the
other reaction conditions (Figure 6, middle), one can calculate
that the supersaturation decreased by 2.7 times, estimated using
eq 11. This should be reflected as a significant change of the
slope in the plot, instead of being constant (Figure 6 left and
middle). Furthermore, according to eq 7a, the intercept should
not change upon changing the acid concentration for nucleation-
controlled formation. These facts imply that, similar to the
results on the reaction orders discussed above, the temperature
dependence of the formation rate of the InP nanoclusters
supported the reaction-controlled mechanism, instead of classic
nucleation-controlled mechanism.
The temperature dependence of the reactions using indium
acetate (In(Ac)3) as the indium precursor was also studied by
varying the ligand (myristic acid) concentration (Figure S4).
In(Ac)3 and other types of metal acetates are the commonly
available metal-organic compounds and have been widely used
directly as the metal precursors for synthesis of high quality
nanocrystals. Because of the very short hydrocarbon chain, long-
chain fatty acids with different concentrations are often added
as the ligands of the resulting nanocrystals. The exact composi-
The above interpretation implies that fatty amines “activate”
metal fatty acid salts by increasing the activation entropy, instead
of decreasing the activation energy. Consistent with this,
although InP nanoclusters could be formed at a temperature
below 100 °C without the presence of amine, the reactions with
amines did not show appreciable formation of InP particles at
(25) Narayanaswamy, A.; Xu, H.; Pradhan, N.; Kim, M.; Peng, X. J. Am.
Chem. Soc. 2006, 128, 10310–10319.
(26) Koo, B.; Patel, R. N.; Korgel, B. A. J. Am. Chem. Soc. 2009, 131,
3134–3135.
9
15464 J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009

Nucleation Kinetics vs Chemical Kinetics
A R T I C L E S
Figure 8. Arrhenius plot of the formation of CdS nanocrystals (left) and the corresponding absorption spectra (middle). UV-vis and photoluminescence
(PL) spectra of as-synthesized CdS nanocrystal sample grown at 180 °C (right) using oleic acid (HOl) as the ligands and CdO as the Cd precursor.
such relatively low temperatures. At a high reaction temperature,
however, the reaction rate for the amine-based reactions
enhanced substantially, which promoted a rapid growth of the
relatively large InP nanocrystals in amine-based reaction sys-
tems.27
CdS Nanocrystals System. The CdS nanocrystals system was
studied to examine the possibilities to extend the above
experimental strategies to other crystallization systems. Similar
to the InP system without amines added, CdS nanocrystals could
be formed with cadmium fatty acid salts (such as cadmium
stearate, Cd(St)2) and elemental S in ODE with fatty acid added
as the only additive.13 For this well developed system, it was
possible to form nearly monodisperse CdS nanocrystals with a
relatively large size (∼2.8 nm) in a quite broad temperature
range (Figure 8, middle).
The reaction order for the formation of the CdS nanocrystals
against the rate limiting precursor, S, was found to be 2 (Figure
S5, Supporting Information). The results in Figure 8 (left) show
that the activation energy for the formation of CdS nanocrystals
under the specified reaction conditions was about 27 kJ/mol.
All of these results indicate that this system can also be well
described using the reaction-controlled formation. Furthermore,
the relatively low activation energy implies that CdS nanocryst-
als could be synthesized at a temperature much below the typical
temperature used for this established reaction system, between
250 and 300 °C.13 Preliminary results indeed confirmed that
high quality CdS nanocrystals could be synthesized at 180 °C
(Figure 8, right).
will end up as a systematic error for the intercept of an Arrhenius
plot and not affect the slope of the linear plot. Equation 14
indicates that activation energy and reaction orders are solely
determined by the slope of the plots under different reaction
conditions. For the intercept, its absolute value may not be
accurate but the difference between the intercepts of two linear
fitting functions (see Figures 6 and S4, Supporting Information)
should still be reliable because systematic errors would be
canceled in calculations of difference.
The reaction rates presented here were all initial reaction rates,
which were calculated by measuring the samples taken at 5 s
after the initial injection of the phosphors (or sulfur) precursor
solution into the reaction solution. The injection/mixing process
took approximately 1 s, and the fastest sampling was about 5 s
manually. The samples were taken with a time inaccuracy of
about 1 s. Evidently, the improvement of accuracy of this
method, that is, determination of formation rates with fixed size
and size distribution, should come from the measurement of
the reaction time, such as an in situ scheme for recording the
absorption spectra. In fact, previous in situ studies9 indicate that
formation of CdSe nanocrystals in a similar reaction system
could last for a few seconds, which means that the current time
accuracy might not be too bad.
Reaction-Controlled Kinetics, Instead of Nucleation-
Controlled Kinetics. The reaction-controlled kinetics, instead
of nucleation-controlled kinetics seemed to be consistent with
the experimental data. As mentioned above, this implies that
chemical reactions should be the rate-determining step in the
systems studied here. According to Figure 1 and the related
discussions, “reaction-controlled formation” might generally be
the dominating path for the synthesis of high quality colloidal
nanocrystals. This is so for two reasons. First, nearly all of the
targeted nanocrystal systems today are extremely insoluble ones
in solvents. Second, when a synthetic scheme was developed,
the precursor concentrations have always been pushed to a high
limit to achieve a high yield in synthesis. These two factors
could allow a system to readily reach an extremely high
supersaturation to justify the “reaction-controlled formation”,
instead of the “nucleation-controlled formation” (Figure 1).
The question is why nucleationscorresponding to “nucleation-
controlled formation” in Figure 1shas historically been well
accepted as the central concept for the formation of crystals
although this region seems to be just one part of the picture.
For crystals with a reasonably high solubility, such as NaCl or
other highly soluble salts in water, the Smax corresponding to
those molecular clusters could be too high to reach for a practical
solution. As a result, “reaction-controlled formation” would
become forbidden. Furthermore, if the solubility is too high,
homogeneous nucleation might also become very difficult to
Discussion
Accuracy. The accuracy on determining the size, shape, size/
shape distribution, and concentration of the initial solid seeds
(nuclei) has been the main obstacle for studying nucleation
process. The results reported here indicate that, under carefully
chosen reaction conditions, it would be possible to solve this
problem by taking advantage of the size-dependent optical
properties of semiconductor nanocrystals/nanoclusters. However,
although it has been possible to generate nanocrystals with a
good control over the size and size distribution, some uncertainty
on these structural parameters shall still exist.
The experimental method demonstrated a possibility to study
formation of nanoclusters/nanocrystals with a fixed size and size
distribution. In this method, any inaccuracy on determining the
size, size distribution, and extinction coefficient would be
eliminated for determining the reaction order and activation
energy. This is so because any inaccuracy on these parameters
(27) Xie, R.; Battaglia, D.; Peng, X. J. Am. Chem. Soc. 2007, 129, 15432–
15433.
9
J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009 15465

A R T I C L E S
Xie et al.
(99%) were purchased from Alfa. All indium fatty acid salts were
prepared in our lab by using the same method reported in
literature.28 All the chemicals were used without further purification.
observe and heterogeneous nucleation (see Figure 1) shall
dominate the system as noticed by Mullen in his famous book.5
There is a reason that causes people to believe nucleation is
a universal picture, even for very insoluble crystals. As
discovered recently, when the concentration of nanocrystals/
nanoclusters reached a certain value, “self-focusing”20,28,29 (see
Theoretical section) might start to occur if the nanoparticles
are somewhat soluble in the solution with the existence of
relatively strong ligands. This process shall stop the further
formation of crystals, which could be mis-interpreted as the
completion of nucleation. On the other hand, if the crystals were
nearly completely insoluble, initial formation of crystals would
be very fast and stop sharply because of the depletion of
monomers. This may be mis-regarded as the completion of
nucleation as well.
It should be pointed out that “magic sized clusters” have often
been mistaken as the critical sized nuclei, at least in synthesis
of semiconductor nanocrystals.12 However, the model in Figure
1 tells us that these local thermodynamic minima could just be
shallow traps in a crystallization system. Inconsistent with the
expectation of critical sized nuclei, further growth of “magic
sized clusters” requires the clusters to overcome a thermody-
namic barrier, namely the barrier on the right side in each
potential trap associated with “magic sized clusters” in Figure
1. Thus, addition of a few structural units to the clusters is
thermodynamically unfavorable, which is why the growth of a
“magic sized cluster” has always been observed to end up a
much larger nanocrystals“forward-tunneling”. Consequently,
the growth of “magic sized clusters” has been observed to be
slow.12,20 However, if these nanoclusters are qualified as critical
sized nuclei, the classic nucleation theory12 would require the
formation of the “magic sized clusters” to be slow and the
following growth to be much faster, which is opposite to the
experimental results.
Synthesis of InP Nanocrystals/Nanoclusters without
Amine. The injection solution of P precursor was prepared by
mixing tris-trimethylsilyl phosphine and ODE (1.0 mL in total) in
a glovebox. For a typical synthesis, In(He)3 (0.4 mmol), hexanoic
acid (1.4 mmol), and 4 g of 1-octadecene (ODE) were loaded into
a three-neck flask. The mixture was heated to 18 °C under argon
flow, and then, the P precursor solution made in glovebox was
injected into the hot reaction mixture. For determining the initial
reaction rate, an aliquots was taken immediately (5 s) after the
injection. The concentration of InP nanocrystals in reaction was
calculated using the Beer’s law by measuring the diluted solution
of the aliquots. To determine the concentration reproducibly, the
amount of reaction mixture was measured using an analytical
balance by mass, while the direct record of volume of the aliquots
was found to be inaccurate.
Synthesis of InP Nanocrystals/Nanoclusters in Presence of
Amines. The injection solution of the P precursor was prepared
by mixing tris-trimethylsilyl phosphine and 2.4 mmol octylamine
in ODE (1.0 mL in total) in a glovebox. For a typical synthesis,
indium acetate (0.4 mmol), myristic acid (1.4 mmol), and 4 g of
1-octadecene (ODE) were loaded into a three-neck flask. The
mixture was heated to 178 °C under argon flow, and then, the P
precursor solution made in glovebox was injected into the hot
reaction mixture. The rest of the procedures were the same as those
described above.
Composition of the Indium Fatty Acid Salts. The composition
of the indium fatty acid salts in the reactions using indium acetate
plus a long chain fatty acid was determined using FTIR method.
In a typical reaction, 0.4 mmol indium acetate, 1.25 mmol myristic
acid and 4 mL ODE were loaded into flask. The mixture was heated
to 188 °C under argon. The sample of the mixture was taken for
FTIR measurement after 5 min. The amount of acid in a given
mixture was determined using a standard myristic acid solution with
known molar concentration in ODE.
Growth of Nanoclusters/Nanocrystals. The growth of nano-
clusters/nanocrystals after their formation is likely size depend-
ent. For example, as mentioned in the above paragraph, the
growth of “magic sized clusters” was found to be particularly
slow. In addition, several known phenomena observed in the
growth stage, such as Ostwald ripening, intraparticle ripening,
and “self-focusing”, are all direct results of the size dependent
chemical stability (reactivity) of the nanoclusters/nanocrystals.
This implies that theoretical treatment of the growth of
nanoclusters/nanocrystals probably should not ignore the size
dependent chemical properties of the particles although the
formation processsnucleation in traditional meaningscould
concentrate on the initial chemical reaction(s).
Synthesis of CdS Nanocrystals. The synthesis of CdS nano-
crystals followed a similar method reported in literature.13 For
determining the activation energy, ODE (4 mL), 0.4 mmol Cd(St)2
and 0.2 mmol SA were loaded into three-neck flask. The mixture
was heated to a given temperature in the range between 240 and
300 °C under argon, then 0.2 mmol S in ODE was injected quickly
into the reaction mixture. An aliquots was taken immediately taken
(about 5 s after the injection) for the measurements of UV-vis
spectrum. The particle concentration was determined using the same
method for the InP nanoclusters/nanocrystals system discussed
above with the extinction coefficients in literature.30
Acknowledgment. This work was partially supported by the
NSF and NIH.
Supporting Information Available: Table of fatty acids,
reaction orders of indium precursor, amines, and sulfur (for CdS
system), as well as the temperature dependence of the formation
rate of InP using In(Ac)3 as the precursor. This material is
available free of charge via the Internet at http://pubs.acs.org.
Experiment Section
Materials. Technical grade (90%) Octadecene (ODE), Indium
acetate (In(Ac)3, 99.99%), Stearic acid (98%), Myristic acid
(99%)Butyric acid (99%), Hexanoic acid (98%), Octanoic acid
(90%), Tris-trimethylsily phosphine (P(TMS)3, 95%), 1-octylamine
JA9063102
(28) Chen, Y.; Johnson, E.; Peng, X. J. Am. Chem. Soc. 2007, 129, 10937–
10947.
(29) Thessing, J.; Qian, J.; Chen, H.; Pradhan, N.; Peng, X. J. Am. Chem.
Soc. 2007, 129, 2736–2737.
(30) Yu, W. W.; Qu, L.; Guo, W.; Peng, X. Chem. Mater. 2003, 15 (14),
2854–2860.
9
15466 J. AM. CHEM. SOC. VOL. 131, NO. 42, 2009